2019-05-24T23:40:02Z http://ijgt.ui.ac.ir/?_action=export&rf=summon&issue=756
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International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2014 3 4 Restrictions on commutativity ratios in finite groups Robert Heffernan Des MacHale Aine Ni She  ‎We consider two commutativity ratios \$Pr(G)\$ and \$f(G)\$ in a finite group \$G\$‎ ‎and examine the properties of \$G\$ when these ratios are `large'‎. ‎We show that‎ ‎if \$Pr(G) > frac{7}{24}\$‎, ‎then \$G\$ is metabelian and we give threshold‎ ‎results in the cases where \$G\$ is insoluble and \$G'\$ is nilpotent‎. ‎We also‎ ‎show that if \$f(G) > frac{1}{2}\$‎, ‎then \$f(G) = frac{n+1}{2n}\$‎, ‎for some‎ ‎natural number \$n\$‎. commutativity ratios commuting probability Finite groups 2014 12 01 1 12 http://ijgt.ui.ac.ir/article_4570_55d0f1553f00e86de09233d4129f5a8f.pdf Math. Proc. R. Ir. Acad. F. Barry 104A 119 2004 Proc. Amer. Math. Soc. Y. Berkovich 121 679 1994 Publ. Math. Debrecan Y. Berkovich and K. R. Nekrasov 33 333 1986 Part 2. Translated from the Russian manuscript by P. Shumyatsky [P. V. Shumyatski{ui}], V. Zobina and Berkovich. Translations of Mathematical Monographs, American Mathematical Society, Providence, RI Ya. G. Berkovich and E. M. Zhmud 181 1999 The University of Chicago Press H. F. Blichfeldt 1917 Proc. Roy. Irish Acad. Sect. A J. Burns, G. Ellis, D. MacHale, P. OMurchu, R. Sheehy, and J. Wiegold 97 113 1997 2d ed. Dover Publications, Inc., New York W. Burnside 1955 Atlas of finite groups. Maximal subgroups and ordinary characters for simple groups, With computational assistance from J. G. Thackray, Oxford University Press, Eynsham J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson 1985 C. R. Math. Acad. Sci. Soc. R. Can. J. D. Dixon 24 1 2002 http://www.icm.tu-bs.de/ag_algebra/software/small/small.html B. Eick, H. U. Besche and E. OBrien Amer. Math. Monthly W. H. Gustafson 80 1031 1973 J. Reine Angew. Math. P. Hall 182 130 1940 Ph.D. thesis, University of California, Los Angeles K. S. Joseph 1969 J. Algebra P. Lescot 177 847 1995 Proc. Roy. Irish Acad. Sect. A D. MacHale and P. OMurchu 93 123 1993 Master's thesis, National University of Ireland, Cork P. OMurchu 1990 Pacific J. Math. D. S. Passman 17 475 1966 Ph. D. thesis, National University of Ireland, Cork A. NiShe 2000 Springer-Verlag T. A. Springer 1977 Mem. Amer. Math. Soc. S. S.-T. Yau and Y. Yu 505 1993
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International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2014 3 4 The unit group of algebra of circulant matrices Neha Makhijani R. K. Sharma J. B. Srivastava Let \$Cr_{n}(F)\$ denote the algebra of \$ntimes n\$ circulant matrices over the field \$F\$‎. ‎In this paper‎, ‎we study the unit group of \$Cr_{n}(mathbb{F}_{p^{m}})\$‎, ‎where \$mathbb{F}_{p^{m}}\$ denotes the Galois field of order \$p^{m},~p\$ prime‎. group algebra Unit Group Circulant Matrices 2014 12 01 13 16 http://ijgt.ui.ac.ir/article_4776_76fd6d2530a88ac6184b7c4c0c57fca7.pdf Comm. Algebra V. Bovdi 29 5411 2001 J. Group Theory V. Bovdi 15 227 2012 Canad. Math. Bull. L. Creedon and J. Gildea 54 237 2011 Acta Math. Acad. Paedagog. Nyhazi. J. Gildea 24 221 2008 Comm. Algebra J. Gildea 38 3311 2010 J. Algebra Appl. J. Gildea 10 643 2011 Int. J. Pure Apl. Math. T. Hurley 31 319 2006 J. Algebra Appl., http://dx.doi.org/10.1142/S0219498813500904 K. Kaur and M. Khan 13 2014 Cambridge University Press R. Lidl and H. Niederreiter 2000 Trans. Amer. Math. Soc. S. Perlis and G. L. Walker 68 420 1950 Kluwer Academic Publishers C. P. Milies and S. K. Sehgal 2002 Int. J. Group Theory R. K. Sharma and P. Yadav 2 1 2013 Int. J. Group Theory R. K. Sharma, P. Yadav and K. Joshi 1 33 2012
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International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2014 3 4 On weakly \$SS\$-quasinormal and hypercyclically embedded properties of finite groups Tao Zhao A subgroup \$H\$ is said to be \$s\$-permutable in a group \$G\$‎, ‎if‎ ‎\$HP=PH\$ holds for every Sylow subgroup \$P\$ of \$G\$‎. ‎If there exists a‎ ‎subgroup \$B\$ of \$G\$ such that \$HB=G\$ and \$H\$ permutes with every‎ ‎Sylow subgroup of \$B\$‎, ‎then \$H\$ is said to be \$SS\$-quasinormal in‎ ‎\$G\$‎. ‎In this paper‎, ‎we say that \$H\$ is a weakly \$SS\$-quasinormal‎ ‎subgroup of \$G\$‎, ‎if there is a normal subgroup \$T\$ of \$G\$ such that‎ ‎\$HT\$ is \$s\$-permutable and \$Hcap T\$ is \$SS\$-quasinormal in \$G\$‎. ‎By‎ ‎assuming that some subgroups of \$G\$ with prime power order have the‎ ‎weakly \$SS\$-quasinormal properties‎, ‎we get some new‎ ‎characterizations about the hypercyclically embedded subgroups of‎ ‎\$G\$‎. ‎A series of known results in the literature are unified and‎ ‎generalized. ‎\$s\$-permutable‎ ‎weakly \$SS\$-quasinormal‎ \$p\$-nilpotent‎ ‎hypercyclically embedded 2014 12 01 17 25 http://ijgt.ui.ac.ir/article_4950_c0915a41877e3a4bb1db406fbaca42cf.pdf J. Pure Appl. Algebra A. Ballester-Bolinches and M. C. Pedraza-Aguilera 127 113 1998 Glasg. Math. J. A. Ballester-Bolinches, Y. Wang and X. Guo 42 383 2000 Math. Z. W. E. Deskins 82 125 1963 Walter de Gruyter, Berlin, New York K. Doerk and T. Hawkes 1992 Chelsea, New York-London D. Gorenstein 1968 Science Press-Kluwer Academic Publishers, New York W. Guo 2000 J. Algebra Discrete Struct. W. Guo, Y. Wang and L. Shi 6 95 2008 Sci. China Ser. A W. Guo, K. P. Shum and A. N. Skiba 52 272 2009 Algebra Log. W. Guo, Y. Lu and W. Niu 49 293 2010 Springer, New York, Berlin B. Huppert 1967 Math. Z. O. H. Kegel 78 205 1962 J. Algebra S. Li, Z. Shen, J. Liu and X. Liu 319 4275 2008 J. Pure Appl. Algebra Y. Li and X. Li 202 72 2005 Commun. Algebra Y. Li, S. Qiao and Y. Wang 37 1086 2009 J. Algebra A. N. Skiba 315 192 2007 J. Pure Appl. Algebra A. N. Skiba 215 257 2011 J. Algebra P. Schmid 207 285 1998 J. Algebra Y. Wang 180 954 1996 Comm. Algebra Y. Wang and W. Guo 38 3821 2010 Proc. Edinb. Math. Soc. (2) H. Wei and Y. Wang 50 493 2007 J. Group Theory H. Wei and Y. Wang 10 211 2007 Polygonal Publishing House H. G. Bray and M. Weinstein 1982
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International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2014 3 4 On zero patterns of characters of finite groups Jinshan Zhang Guangju Zeng Zhencai Shen The aim of this note is to characterize the finite‎ ‎groups in which all non-linear irreducible characters have distinct zero entries number‎. Finite groups characters zeros of characters 2014 12 01 27 31 http://ijgt.ui.ac.ir/article_4952_63eb74c1c94bc55ca2353308a1051eba.pdf Proc. Amer. Math. Soc. Y. Berkovich, D. Chillag and M. Herzog 115 955 1992 Illinois J. Math. W. Feit and G. M. Seitz 33 103 1989 Pacific J. Math. S. M. Gagola 109 363 1983 Academic Prees, New York I. M. Isaacs 1976 J. Algebra I. M. Isaacs, G. Navarro and T. R. Wolf 222 413 1999 Ann. Uni. Sci. Budapest. E"{o}tv"{o}s Sect. Math. P. P. Pacutealfy 24 181 1981 Chinese Ann. Math. Ser. B Y. C. Ren and X. Y. Li 21 511 2000 Oxford University Press, Eynsham J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Park and R. A. Wilson 1985 J. Algebra Appl. J. S. Zhang, Z. C. Shen and S. L. Wu 12 1 2013
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International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2014 3 4 A note on the normalizer of Sylow \$2\$-subgroup of special linear‎ ‎group \${rm SL}_2(p^f)\$ Jiangtao Shi Let \$G={rm SL}_2(p^f)\$ be a special linear group and \$P\$ be a Sylow‎ ‎\$2\$-subgroup of \$G\$‎, ‎where \$p\$ is a prime and \$f\$ is a positive‎ ‎integer such that \$p^f>3\$‎. ‎By \$N_G(P)\$ we denote the normalizer of‎ ‎\$P\$ in \$G\$‎. ‎In this paper‎, ‎we show that \$N_G(P)\$ is nilpotent (or‎ ‎\$2\$-nilpotent‎, ‎or supersolvable) if and only if \$p^{2f}equiv‎ ‎1,({rm mod},16)\$‎. special linear group Sylow subgroup normalizer nilpotent supersolvable 2014 12 01 33 36 http://ijgt.ui.ac.ir/article_4976_a69c9b523546d6cc0812f1d9027240e7.pdf Springer-Verlag, Berlin B. Huppert 1967 (Second Edition), Springer-Verlag, New York D. J. S. Robinson 1996
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International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2014 3 4 On one class of modules over group rings with finiteness restrictions Olga Dashkova The author studies the \$bf R\$\$G\$-module \$A\$ such that \$bf R\$ is an associative ring‎, ‎a group \$G\$ has infinite section \$p\$-rank (or infinite 0-rank)‎, ‎\$C_{G}(A)=1\$‎, ‎and for every‎ ‎proper subgroup \$H\$ of infinite section \$p\$-rank (or infinite 0-rank respectively) the quotient module \$A/C_{A}(H)\$ is‎ ‎a finite \$bf R\$-module‎. ‎It is proved that if the group \$G\$ under‎ ‎consideration is locally soluble‎ ‎then \$G\$ is a soluble group and \$A/C_{A}(G)\$ is a finite \$bf R\$-module‎. ‎ group ring linear group module 2014 12 01 37 46 http://ijgt.ui.ac.ir/article_5087_ca4189aa5efbaeed67562c6122922f8a.pdf Illinois J. Math. R. Baer and H. Heineken 16 533 1972 Asian-Eur. J. Math. O. Yu. Dashkova 3 45 2010 J. Math. Sci. (N. Y.) O. Yu. Dashkova 169 636 2010 Ukrainian Math. J. O. Yu. Dashkova 63 1379 2012 Siberian Adv. Math. O. Yu. Dashkova 23 77 2013 J. Pure Appl. Algebra O. Yu. Dashkova, M. R. Dixon and L. A. Kurdachenko 208 785 2007 J. Algebra M. R. Dixon, M. J. Evans and L. A. Kurdachenko 277 172 2004 J. Algebra S. Franciosi, F. De Giovanni and L. A. Kurdachenko 174 823 1995 (in Ukrainian), Uzhgorod: Uzhgorodskii Natsionalnii Universitet P. M. Gudivok, V. P. Rud’ko and V. A. Bovdi 174 2006 (in Russian), Moscow, Nauka M. I. Kargapolov and Yu. I. Merzlyakov 1975 North-Holland Mathematical Library, North-Holland Publishing Co., Amsterdam, London O. H. Kegel and B. A. F. Wehrfritz 3 1973 (Russian), Infinite groups and adjoining algebraic structures (Russian), Akad. Nauk Ukrainy, Inst. Mat., Kiev L. A. Kurdachenko 160 1993 (Russian), Mat. Sbornik N.S. A. I. Malcev 22 351 1948 Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, New York-Berlin D. J. R. Robinson 1,2 1972 Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer-Verlag, New York, Heidelberg, Berlin B. A. F. Wehrfritz 1973
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International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2014 3 4 Quasirecognition by prime graph of finite simple groups \${}^2D_n(3)\$ Behrooz Khosravi Hossein Moradi ‎Let \$G\$ be a finite group‎. ‎In [Ghasemabadi et al.‎, ‎characterizations of the simple group \${}^2D_n(3)\$ by prime graph‎ ‎and spectrum‎, ‎Monatsh Math.‎, ‎2011] it is‎ ‎proved that if \$n\$ is odd‎, ‎then \${}^2D _n(3)\$ is recognizable by‎ ‎prime graph and also by element orders‎. ‎In this paper we prove‎ ‎that if \$n\$ is even‎, ‎then \$D={}^2D_{n}(3)\$ is quasirecognizable by‎ ‎prime graph‎, ‎i.e‎. ‎every finite group \$G\$ with \$Gamma(G)=Gamma(D)\$‎ ‎has a unique nonabelian composition factor and this factor is isomorphic to‎ ‎\$D\$‎. Prime graph simple group linear group quasirecognition 2014 12 01 47 56 http://ijgt.ui.ac.ir/article_5254_b31e2bb7e4d6f7188c9fd129dd78758f.pdf Sib. Math. J. A. Babai and B. Khosravi 52 788 2011 Bull. Malays. Math. Sci. Soc. (2) A. Babai, B. Khosravi and N. Hasani 32 343 2009 Oxford University Press, Oxford J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson 1985 Monatsh Math. M. F. Ghasemabadi, A. Iranmanesh and N. Ahanjideh 168 347 2012 Publ. Math. Debrecen B. Khosravi, Z. Akhlaghi and M. Khatami 78 469 2011 Acta Math. Hungar. B. Khosravi and H. Moradi 132 140 2011 J. Algebra Appl. B. Khosravi and H. Moradi 11 15 2012 Monatsh Math. Z. Momen and B. Khosravi 166 239 2012 Sib. Math. J. A. V. Vasilev 46 396 2005 Sib. Math. J. A. V. Vasil'ev and I. B. Gorshkov 50 233 2009 Algebra Logic A. V. Vasil'ev and E. P. Vdovin 44 381 2005 Algebra Logic, Arxiv: 0905.1164v1 A. V. Vasil'ev and E. P. Vdovin 50 291 2011 Monatsh. Math. Phys. K. Zsigmondy 3 265 1892
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International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2014 3 4 A note on fixed points of automorphisms of infinite groups Francesco de Giovanni Martin L. Newell Alessio Russo ‎Motivated by a celebrated theorem of Schur‎, ‎we show that if \$Gamma\$ is a normal subgroup of the full automorphism group \$Aut(G)\$ of a group \$G\$ such that \$Inn(G)\$ is contained in \$Gamma\$ and \$Aut(G)/Gamma\$ has no uncountable abelian subgroups of prime exponent‎, ‎then \$[G,Gamma]\$ is finite‎, ‎provided that the subgroup consisting of all elements of \$G\$ fixed by \$Gamma\$ has finite index‎. ‎Some applications of this result are also given.‎ automorphism group Schur's theorem absolute centre 2014 12 01 57 61 http://ijgt.ui.ac.ir/article_5342_1e6c5c18b97f38824f43a2febfd71900.pdf Math. Ann. R. Baer 124 161 1952 J. Algebra H. Dietrich and P. Moravec 341 150 2011 Arch. Math. (Basel) S. Franciosi and F. de Giovanni 47 12 1986 J. Algebra P. Hegarty 169 929 1994 Springer, Berlin D. J. S. Robinson 1972 J. Reine Angew. Math. I. Schur 127 20 1904 Proc. London Math. Soc. (3) R. F. Turner Smith 14 321 1964 Quart. J. Math. Oxford Ser. (2) D. J. S. Robinson 30 351 1979
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International Journal of Group Theory Int. J. Group Theory 2251-7650 2251-7650 2014 3 4 Symmetry classes of polynomials associated with the ‎direct ‎product of permutation groups Esmaeil Babaei Yousef Zamani ‎Let \$G_{i} \$ be a subgroup of \$ S_{m_{i}}‎ ,‎ 1 leq i leq k\$‎. ‎Suppose \$chi_{i}\$ is an irreducible complex character of \$G_{i}\$‎. ‎We consider \$ G_{1}times cdots times G_{k} \$ as subgroup of \$ S_{m} \$‎, ‎where \$ m=m_{1}+cdots‎ +‎m_{k} \$‎. ‎In this paper‎, ‎we give a formula for the dimension of \$H_{d}(G_{1}times cdots times G_{k}‎, ‎chi_{1}timescdots times chi_{k})\$ and investigate the existence of an o-basis of this type of classes‎. Symmetric polynomials symmetry class of polynomials‎ ‎orthogonal basis ‎permutaion groups‎ ‎complex characters 2014 12 01 63 69 http://ijgt.ui.ac.ir/article_5479_0495fb15f251988634840c9c7812f01e.pdf to appear in Bull. Iranian Math. Soc. E. Babaei and Y. Zamani Linear and Multilinear Algebra M. R. Darafsheh and M. R. Pournaki 47 137 2000 SUT J. Math. M. R. Darafsheh and N. S. Poursalavati 37 1 2001 Linear and Multilinear Algebra R. R. Holmes 39 241 1995 Academic Press, New York I. M. Isaacs 1976 Gordon and Breach Science Publisher, Amsterdam R. Merris 1997 Linear Algebra Appl. M. Shahryari 433 1410 2010 J. Algebra M. Shahryari 220 327 1999 Asian-Eur. J. Math. M. Shahryari and Y. Zamani 4 179 2011 J. Algebra Appl., (10 pages) Y. Zamani and E. Babaei 13 2014 Pure Math. Appl. Y. Zamani 18 357 2007 Asian-Eur. J. Math., (10 pages) Y. Zamani and E. Babaei 6 2013