University of IsfahanInternational Journal of Group Theory2251-76502320130901On the order of the Schur multiplier of a pair of finite p-groups II18200710.22108/ijgt.2013.2007ENFahimehMohammadzadehPayame Noor University of IranAzamHokmabadiPayame Noor University of IranBehroozMashayekhyFerdowsi University of MashhadJournal Article20120413Let $G$ be a finite $p$-group and $N$ be a normal subgroup of $G$ with $|N|=p^n$ and $|G/N|=p^m$. A result of Ellis (1998) shows that the order of the Schur multiplier of such a pair $(G,N)$ of finite $p$-groups is bounded by $ p^{\frac{1}{2}n(2m+n-1)}$ and hence it is equal to $ p^{\frac{1}{2}n(2m+n-1)-t}$ for some non-negative integer $t$. Recently, the authors have characterized the structure of $(G,N)$ when $N$ has a complement in $G$ and $t\leq 3$. This paper is devoted to classification of pairs $(G,N)$ when $N$ has a normal complement in $G$ and $t=4,5$.https://ijgt.ui.ac.ir/article_2007_21cfdbdb330703297453c7ae8d688385.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502320130901A note on finite C-tidy groups917200910.22108/ijgt.2013.2009ENSekhar JyotiBaishyaNorth-eastern Hill UniversityJournal Article20121002Let $G$ be a group and $x \in G$. The cyclicizer of $x$ is defined to be the subset $Cyc(x)=\lbrace y \in G \mid \langle x, y\rangle \; {\rm is \; cyclic} \rbrace$. $G$ is said to be a tidy group if $Cyc(x)$ is a subgroup for all $x \in G$. We call $G$ to be a C-tidy group if $Cyc(x)$ is a cyclic subgroup for all $x \in G \setminus K(G)$, where $K(G)$ is the intersection of all the cyclicizers in $G$. In this note, we classify finite C-tidy groups with $K(G)=\lbrace 1 \rbrace$.https://ijgt.ui.ac.ir/article_2009_40492b1ec662d802b7e99ceac68fc720.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502320130901The Fischer-Clifford matrices of the inertia group 27:O- 6 (2) of a maximal subgroup 27:Sp6(2) in sp8(2)1938204910.22108/ijgt.2013.2049ENAbrahamPrinsStellenbosch UniversityRichardFrayUniversity of the Western CapeJournal Article20121114The subgroups of symplectic groups which fix a non-zero vector of the underlying symplectic space are called <em>affine subgroups.,</em> The split extension group $A(4)\cong 2^7{:}Sp_6(2)$ is the affine subgroup of the symplectic group $Sp_8(2)$ of index $255$. In this paper, we use the technique of the Fischer-Clifford matrices to construct the character table of the inertia group $2^7{:}O^{-}_{6}(2)$ of $A(4)$ of index $28$.https://ijgt.ui.ac.ir/article_2049_7354cfb13c7d59221a89e0a3fa22f5a4.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502320130901On normal automorphisms of n-periodic products of finite cyclic groups3947234810.22108/ijgt.2013.2348ENVaruzhanAtabekyanDepartment of Mathematics and mekhanics Yerevan State UniversityAmirjanGevorgyanDepartment of Applied Mathematics, Russian-Armenian Slavonic UniversityAniKhachatryanDepartment of Mathematics and Mechanics, Yerevan State UniversityAshotPahlevanyanDepartment of Mathematics and Mechanics, Yerevan State UniversityJournal Article20120210We prove that each normal automorphism of the $n$-periodic product of cyclic groups of odd order $rge1003$ is inner, whenever $r$ divides $n$.https://ijgt.ui.ac.ir/article_2348_55fb21e333e0650958ddb1d486ac2f47.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502320130901Enumerating algebras over a finite field4961244010.22108/ijgt.2013.2440ENMichaelVaughan-LeeOxford University
Mathematical InstituteJournal Article20121204We obtain the PORC formulae for the number of non-associative algebras of dimension 2, 3 and 4 over the finite field GF$(q)$. We also give some asymptotic bounds for the number of algebras of dimension $n$ over GF$(q)$.https://ijgt.ui.ac.ir/article_2440_9d9a3a7f721dfec413b8c9c171e8ac89.pdfUniversity of IsfahanInternational Journal of Group Theory2251-76502320130901Finite groups with some $SS$-embedded subgroups6370254310.22108/ijgt.2013.2543ENTaoZhaoSchool of Science, Shandong University of TechnologyJournal Article20120704We call $H$ an $SS$-embedded subgroup of $G$ if there exists a normal subgroup $T$ of $G$ such that $HT$ is subnormal in $G$ and $H\cap T\leq H_{sG}$, where $H_{sG}$ is the maximal $s$-permutable subgroup of $G$ contained in $H$. In this paper, we investigate the influence of some $SS$-embedded subgroups on the structure of a finite group $G$. Some new results were obtained.https://ijgt.ui.ac.ir/article_2543_06ac8fa1eb432b06922a796f102b6e80.pdf