International Journal of Group TheoryInternational Journal of Group Theory
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Fri, 18 Jan 2019 14:18:40 +0100FeedCreatorInternational Journal of Group Theory
http://ijgt.ui.ac.ir/
Feed provided by International Journal of Group Theory. Click to visit.A probabilistic version of a theorem\\ of L\'{a}szl\'{o} Kov\'{a}cs and Hyo-Seob Sim
http://ijgt.ui.ac.ir/article_23073_0.html
For a finite group group‎, ‎denote by $mathcal V(G)$ the smallest positive integer $k$ with the property that the probability of generating $G$ by $k$ randomly chosen elements is at least $1/e.$ Let $G$ be a finite soluble group‎. ‎{Assume} that for every $pin pi(G)$ there exists $G_pleq G$ such that $p$ does not divide $|G:G_p|$ and ${mathcal V}(G_p)leq d.$ Then ${mathcal V}(G)leq d+7.$‎Mon, 19 Nov 2018 20:30:00 +0100On some generalization of the malnormal subgroups
http://ijgt.ui.ac.ir/article_23126_0.html
In this paper we obtain a description of finite and certain infinitegroups, whose subgroups are malonormal.Sat, 08 Dec 2018 20:30:00 +01004-Quasinormal subgroups of prime order
http://ijgt.ui.ac.ir/article_23127_0.html
‎Generalizing the concept of quasinormality‎, ‎a subgroup $H$ of a group $G$ is said to be 4-quasinormal in $G$ if‎, ‎for all cyclic subgroups $K$ of $G$‎, ‎$langle H,Krangle=HKHK$‎. ‎An intermediate concept would be 3-quasinormality‎, ‎but in finite $p$-groups‎ - ‎our main concern‎ - ‎this is equivalent to quasinormality‎. ‎Quasinormal subgroups have many interesting properties and it has been shown that some of them can be extended to 4-quasinormal subgroups‎, ‎particularly in finite‎
‎$p$-groups‎. ‎However‎, ‎even in the smallest case‎, ‎when $H$ is a 4-quasinormal subgroup of order $p$ in a finite $p$-group $G$‎, ‎precisely how $H$ is embedded in $G$‎ ‎is not immediately obvious‎. ‎Here we consider one of these questions regarding the commutator subgroup $[H,G]$‎.Sat, 08 Dec 2018 20:30:00 +0100Finite groups with seminormal or abnormal Sylow subgroups
http://ijgt.ui.ac.ir/article_23213_0.html
Let $G$ be a finite group in which every Sylow subgroup is seminormal or abnormal. We prove that $G$ has a Sylow tower. We establish that if a group has a maximal subgroup with Sylow subgroups under the same conditions, then this group is soluble.Sun, 06 Jan 2019 20:30:00 +0100The one-prime power hypothesis for conjugacy classes restricted to normal subgroups and ...
http://ijgt.ui.ac.ir/article_23001_4261.html
We say that a group $G$ satisfies the one-prime power hypothesis for conjugacy classes if the greatest common divisor for all pairs of distinct conjugacy class sizes are prime powers‎. ‎Insoluble groups which satisfy the one-prime power hypothesis have been classified‎. ‎However it has remained an open question whether the one-prime power hypothesis is inherited by normal subgroups and quotients groups‎. ‎In this note we construct examples to show the one-prime power hypothesis is not necessarily inherited by normal subgroups or quotient groups‎.Sat, 30 Nov 2019 20:30:00 +0100Further rigid triples of classes in $G_{2}$
http://ijgt.ui.ac.ir/article_23002_4261.html
We establish the existence of two rigid triples of conjugacy classes in the algebraic group G2 in characteristic 5, complementing results of the second author with Liebeck and Marion. As a corollary, the finite groups G2(5^n) are not (2,4,5)-generated, confirming a conjecture of Marion in this case.Sat, 30 Nov 2019 20:30:00 +0100Graham Higman's PORC theorem
http://ijgt.ui.ac.ir/article_23003_4261.html
Graham Higman published two important papers in 1960‎. ‎In the first of these‎ ‎papers he proved that for any positive integer $n$ the number of groups of‎ ‎order $p^{n}$ is bounded by a polynomial in $p$‎, ‎and he formulated his famous‎ ‎PORC conjecture about the form of the function $f(p^{n})$ giving the number of‎ ‎groups of order $p^{n}$‎. ‎In the second of these two papers he proved that the‎ ‎function giving the number of $p$-class two groups of order $p^{n}$ is PORC‎. ‎He established this result as a corollary to a very general result about‎ ‎vector spaces acted on by the general linear group‎. ‎This theorem takes over a‎ ‎page to state‎, ‎and is so general that it is hard to see what is going on‎. ‎Higman's proof of this general theorem contains several new ideas and is quite‎ ‎hard to follow‎. ‎However in the last few years several authors have developed‎ ‎and implemented algorithms for computing Higman's PORC formulae in‎ ‎special cases of his general theorem‎. ‎These algorithms give perspective on‎ ‎what are the key points in Higman's proof‎, ‎and also simplify parts of the proof‎. ‎In this note I give a proof of Higman's general theorem written in the light‎ ‎of these recent developments‎.Sat, 30 Nov 2019 20:30:00 +0100Limits of generalized quaternion groups
http://ijgt.ui.ac.ir/article_23004_4261.html
‎In the space of marked group‎, ‎we determine the structure of groups which are limit points of the set of all generalized quaternion groups‎.Sat, 30 Nov 2019 20:30:00 +0100Classifying families of character degree graphs of solvable groups
http://ijgt.ui.ac.ir/article_23008_4261.html
‎We investigate prime character degree graphs of solvable groups‎. ‎In particular‎, ‎we consider a family of graphs $Gamma_{k,t}$ constructed by adjoining edges between two complete graphs in a one-to-one fashion‎. ‎In this paper we determine completely which graphs $Gamma_{k,t}$ occur as the prime character degree graph of a solvable group‎.Sat, 30 Nov 2019 20:30:00 +0100