On the order of the schur multiplier of a pair of finite $p$-groups II Fahimeh Mohammadzadeh Payame Noor University of Iran author Azam Hokmabadi Payame Noor University of Iran author Behrooz Mashayekhy Ferdowsi University of Mashhad author text article 2013 eng ‎Let $G$ 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 $t=4,5$‎. International Journal of Group Theory University of Isfahan 2251-7650 2 v. 3 no. 2013 1 8 http://ijgt.ui.ac.ir/article_2007_21cfdbdb330703297453c7ae8d688385.pdf dx.doi.org/10.22108/ijgt.2013.2007 A note on finite C-tidy groups Sekhar Baishya North-eastern Hill University author text article 2013 eng Let $G$ 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 $K(G)=\lbrace 1 \rbrace$‎. International Journal of Group Theory University of Isfahan 2251-7650 2 v. 3 no. 2013 9 17 http://ijgt.ui.ac.ir/article_2009_40492b1ec662d802b7e99ceac68fc720.pdf dx.doi.org/10.22108/ijgt.2013.2009 The Fischer-Clifford matrices of the inertia group $2^7{:}O^{-}_{6}(2)$ of a maximal subgroup $2^7{:}Sp_6(2)$ in $Sp_8(2)$ Abraham Prins Stellenbosch University author Richard Fray University of the Western Cape author text article 2013 eng The subgroups of symplectic groups which fix a non-zero vector of the underlying symplectic space are called affine subgroups., 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 $28$‎. International Journal of Group Theory University of Isfahan 2251-7650 2 v. 3 no. 2013 19 38 http://ijgt.ui.ac.ir/article_2049_7354cfb13c7d59221a89e0a3fa22f5a4.pdf dx.doi.org/10.22108/ijgt.2013.2049 On normal automorphisms of $n$-periodic products of finite cyclic groups Varuzhan Atabekyan Department of Mathematics and mekhanics Yerevan State University author Amirjan Gevorgyan Department of Applied Mathematics, Russian-Armenian Slavonic University author Ani Khachatryan Department of Mathematics and Mechanics, Yerevan State University author Ashot Pahlevanyan Department of Mathematics and Mechanics, Yerevan State University author text article 2013 eng We prove that each normal automorphism of the $n$-periodic product of cyclic groups of odd order $rge1003$ is inner, whenever $r$ divides $n$. International Journal of Group Theory University of Isfahan 2251-7650 2 v. 3 no. 2013 39 47 http://ijgt.ui.ac.ir/article_2348_55fb21e333e0650958ddb1d486ac2f47.pdf dx.doi.org/10.22108/ijgt.2013.2348 Enumerating algebras over a finite field Michael Vaughan-Lee Oxford University Mathematical Institute author text article 2013 eng ‎We 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$(q)$‎. International Journal of Group Theory University of Isfahan 2251-7650 2 v. 3 no. 2013 49 61 http://ijgt.ui.ac.ir/article_2440_9d9a3a7f721dfec413b8c9c171e8ac89.pdf dx.doi.org/10.22108/ijgt.2013.2440 Finite groups with some $SS$-embedded subgroups Tao Zhao School of Science, Shandong University of Technology author text article 2013 eng We 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.‎ International Journal of Group Theory University of Isfahan 2251-7650 2 v. 3 no. 2013 63 70 http://ijgt.ui.ac.ir/article_2543_06ac8fa1eb432b06922a796f102b6e80.pdf dx.doi.org/10.22108/ijgt.2013.2543