Refined solvable presentations for polycyclic groups
René
Hartung
author
Gunnar
Traustason
author
text
article
2012
eng
We describe a new type of presentation that, when consistent, describes a polycyclic group. This presentation is obtained by refining a series of normal subgroups with abelian sections. These presentations can be described effectively in computer-algebra-systems like $ Gap$ or $ Magma$. We study these presentations and, in particular, we obtain consistency criteria for them. The consistency implementation demonstrates that there are situations where the new method is faster than the existing methods for polycyclic groups.
International Journal of Group Theory
University of Isfahan
2251-7650
1
v.
2
no.
2012
1
17
http://ijgt.ui.ac.ir/article_452_1d810507574aaf0c521c12a424179a4e.pdf
dx.doi.org/10.22108/ijgt.2012.452
Some special classes of n-abelian groups
Costantino
Delizia
Dipartimento di Matematica
Università di Salerno - Italy
author
Antonio
Tortora
Dipartimento di Matematica,
Università di Salerno - Italy
author
text
article
2012
eng
Given an integer $n$, we denote by $\mathfrak B_n$ and $\mathfrak C_n$ the classes of all groups $G$ for which the map $\phi_{n}:g\mapsto g^n$ is a monomorphism and an epimorphism of $G$, respectively. In this paper we give a characterization for groups in $\mathfrak B_n$ and for groups in $\mathfrak C_n$. We also obtain an arithmetic description of the set of all integers $n$ such that a group $G$ is in $\mathfrak B_n\cap\mathfrak C_n$.
International Journal of Group Theory
University of Isfahan
2251-7650
1
v.
2
no.
2012
19
24
http://ijgt.ui.ac.ir/article_474_8c61e9cf538261805804cae1cfb096f9.pdf
dx.doi.org/10.22108/ijgt.2012.474
Groups with reality and conjugacy conditions
David
Chillag
author
Patrizia
Longobardi
Dipartimento di Matematica
Universit`a di Salerno
Via Ponte don Melillo 84084 - Fisciano (SA), Italy
author
Mercede
Maj
author
text
article
2012
eng
Many results were proved on the structure of finite groups with some restrictions on their real elements and on their conjugacy classes. We generalize a few of these to some classes of infinite groups. We study groups in which real elements are central, groups in which real elements are $2$-elements, groups in which all non-trivial classes have the same finite size and $FC$-groups with two non-trivial conjugacy class sizes.
International Journal of Group Theory
University of Isfahan
2251-7650
1
v.
2
no.
2012
25
38
http://ijgt.ui.ac.ir/article_715_6f754fe72c9779f6e33f857d2399a1c3.pdf
dx.doi.org/10.22108/ijgt.2012.715
The prolongation of central extensions
Nguyen
Tien Quang
136 Xuanthuy Street, Cau Giay district
author
Che Thi Kim
Phung
Department of
Mathematics and Applications, Saigon University
author
Pham Thi
Cuc
Natural Science Department, Hongduc University, Thanhhoa, Vietnam
author
text
article
2012
eng
The aim of this paper is to study the $(\alpha, \gamma)$-prolongation of central extensions. We obtain the obstruction theory for $(\alpha, \gamma)$-prolongations and classify $(\alpha, \gamma)$-prolongations thanks to low-dimensional cohomology groups of groups.
International Journal of Group Theory
University of Isfahan
2251-7650
1
v.
2
no.
2012
39
49
http://ijgt.ui.ac.ir/article_740_3aee68490b43ff78d1ad06701ebbd4e0.pdf
dx.doi.org/10.22108/ijgt.2012.740
On $p$-soluble groups with a generalized $p$-central or powerful Sylow $p$-subgroup
Evgeny
Khukhro
Sobolev Institute of Mathematics, Novosibirsk
author
text
article
2012
eng
Let $G$ be a finite $p$-soluble group, and $P$ a Sylow $p$-subgroup of $G$. It is proved that if all elements of $P$ of order $p$ (or of order ${}\leq 4$ for $p=2$) are contained in the $k$-th term of the upper central series of $P$, then the $p$-length of $G$ is at most $2m+1$, where $m$ is the greatest integer such that $p^m-p^{m-1}\leq k$, and the exponent of the image of $P$ in $G/O_{p',p}(G)$ is at most $p^m$. It is also proved that if $P$ is a powerful $p$-group, then the $p$-length of $G$ is equal to 1.
International Journal of Group Theory
University of Isfahan
2251-7650
1
v.
2
no.
2012
51
57
http://ijgt.ui.ac.ir/article_761_a54f9c582725efbbb45bb105f241bdb7.pdf
dx.doi.org/10.22108/ijgt.2012.761
The automorphism group for $p$-central $p$-groups
Anitha
Thillaisundaram
University of Cambridge, UK
author
text
article
2012
eng
A $p$-group $G$ is $p$-central if $G^{p}\le Z(G)$, and $G$ is $p^{2}$-abelian if $(xy)^{p^{2}}=x^{p^{2}}y^{p^{2}}$ for all $x,y\in G$. We prove that for $G$ a finite $p^{2}$-abelian $p$-central $p$-group, excluding certain cases, the order of $G$ divides the order of $\text{Aut}(G)$.
International Journal of Group Theory
University of Isfahan
2251-7650
1
v.
2
no.
2012
59
71
http://ijgt.ui.ac.ir/article_745_3af64e999e5c9266e6ec3a1c2db53152.pdf
dx.doi.org/10.22108/ijgt.2012.745