Non-nilpotent groups with three conjugacy classes of non-normal subgroups
Hamid
Mousavi
Department of Mathematics,
University of Tabriz,
P.O.Box 51666-17766,
Tabriz, Iran
author
text
article
2014
eng
For a finite group $G$ let $\nu(G)$ denote the number of conjugacy classes of non-normal subgroups of $G$. The aim of this paper is to classify all the non-nilpotent groups with $\nu(G)=3$.
International Journal of Group Theory
University of Isfahan
2251-7650
3
v.
2
no.
2014
1
7
http://ijgt.ui.ac.ir/article_3533_0e6fd95d96bb53d56958d1ad81586935.pdf
dx.doi.org/10.22108/ijgt.2014.3533
Second cohomology of Lie rings and the Schur multiplier
Max
Horn
AG Algebra,
Mathematisches Institut,
Justus-Liebig-Universität Gießen,
Arndtstrasse 2
35392, Giessen, Germany
author
Seiran
Zandi
Department of Mathematics, University of Kharazmi,
P.O.Box 15614, Tehran, Iran
author
text
article
2014
eng
We exhibit an explicit construction for the second cohomology group $H^2(L, A)$ for a Lie ring $L$ and a trivial $L$-module $A$. We show how the elements of $H^2(L, A)$ correspond one-to-one to the equivalence classes of central extensions of $L$ by $A$, where $A$ now is considered as an abelian Lie ring. For a finite Lie ring $L$ we also show that $H^2(L, C^*) \cong M(L)$, where $M(L)$ denotes the Schur multiplier of $L$. These results match precisely the analogue situation in group theory.
International Journal of Group Theory
University of Isfahan
2251-7650
3
v.
2
no.
2014
9
20
http://ijgt.ui.ac.ir/article_3589_cf135f0fb1340cca48124481e4a34726.pdf
dx.doi.org/10.22108/ijgt.2014.3589
The Fischer-Clifford matrices of an extension group of the form 2^7:(2^5:S_6)
Abraham
Prins
Stellenbosch University
author
Richard
Fray
University
of the Western Cape
author
text
article
2014
eng
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 $2^7{:}(2^5{:}S_{6})$ of $A(4)$ of index $63$.
International Journal of Group Theory
University of Isfahan
2251-7650
3
v.
2
no.
2014
21
39
http://ijgt.ui.ac.ir/article_3659_db2229030defd2c35f47cd2cd8fb7539.pdf
dx.doi.org/10.22108/ijgt.2014.3659
Group actions related to non-vanishing elements
Thomas
Wolf
Ohio University
author
text
article
2014
eng
We characterize those groups $G$ and vector spaces $V$ such that $V$ is a faithful irreducible $G$-module and such that each $v$ in $V$ is centralized by a $G$-conjugate of a fixed non-identity element of the Fitting subgroup $F(G)$ of $G$. We also determine those $V$ and $G$ for which $V$ is a faithful quasi-primitive $G$-module and $F(G)$ has no regular orbit. We do use these to show in some cases that a non-vanishing element lies in $F(G)$.
International Journal of Group Theory
University of Isfahan
2251-7650
3
v.
2
no.
2014
41
51
http://ijgt.ui.ac.ir/article_3669_cb1c4398181ca2cb64256d56ddd3c56c.pdf
dx.doi.org/10.22108/ijgt.2014.3669
Rational subsets of finite groups
Roger
Alperin
San Jose State University
author
text
article
2014
eng
We characterize the rational subsets of a finite group and discuss the relations to integral Cayley graphs.
International Journal of Group Theory
University of Isfahan
2251-7650
3
v.
2
no.
2014
53
55
http://ijgt.ui.ac.ir/article_3780_18c76f677b0c46982874a6daadc10aec.pdf
dx.doi.org/10.22108/ijgt.2014.3780
Conjectures on the normal covering number of finite symmetric and alternating groups
Daniela
Bubboloni
University of Firenze
author
Cheryl E.
Praeger
The University of Western Australia
author
Pablo
Spiga
University of Milano-Bicocca
author
text
article
2014
eng
Let $\gamma(S_n)$ be the minimum number of proper subgroups $H_i,\ i=1, \dots, l $ of the symmetric group $S_n$ such that each element in $S_n$ lies in some conjugate of one of the $H_i.$ In this paper we conjecture that $$\gamma(S_n)=\frac{n}{2}\left(1-\frac{1}{p_1}\right) \left(1-\frac{1}{p_2}\right)+2,$$ where $p_1,p_2$ are the two smallest primes in the factorization of $n\in\mathbb{N}$ and $n$ is neither a prime power nor a product of two primes. Support for the conjecture is given by a previous result for $n=p_1^{\alpha_1}p_2^{\alpha_2},$ with $(\alpha_1,\alpha_2)\neq (1,1)$. We give further evidence by confirming the conjecture for integers of the form $n=15q$ for an infinite set of primes $q$, and by reporting on a $ Magma$ computation. We make a similar conjecture for $\gamma(A_n)$, when $n$ is even, and provide a similar amount of evidence.
International Journal of Group Theory
University of Isfahan
2251-7650
3
v.
2
no.
2014
57
75
http://ijgt.ui.ac.ir/article_3781_473bef8f89b0aadff416858b62a9ac31.pdf
dx.doi.org/10.22108/ijgt.2014.3781