eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2015-09-01
4
3
1
5
9970
On central endomorphisms of a group
Alessio Russo
alessio.russo@unina2.it
1
Seconda Universita di Napoli
Let $Gamma$ be a normal subgroup of the full automorphism group $Aut(G)$ of a group $G$, and assume that $Inn(G)leq Gamma$. An endomorphism $sigma$ of $G$ is said to be $Gamma$-central if $sigma$ induces the the identity on the factor group $G/C_G(Gamma)$. Clearly, if $Gamma=Inn(G)$, then a $Gamma$-central endomorphism is a central endomorphism. In this article the conditions under which a $Gamma$-central endomorphism of a group is an automorphism are investigated.
http://ijgt.ui.ac.ir/article_9970_ca5566bf28c2bba5f0b9d963287fbb1c.pdf
central endomorphism
autocentral endomorphism
purely non-abelian group
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2015-09-01
4
3
7
12
10515
Sandwich classification theorem
Alexey Stepanov
stepanov239@gmail.com
1
St.Petersburg State University
The present note arises from the author's talk at the conference ``Ischia Group Theory 2014''. For subgroups $Fle N$ of a group $G$ denote by $L(F,N)$ the set of all subgroups of $N$, containing $F$. Let $D$ be a subgroup of $G$. In this note we study the lattice $LL=L(D,G)$ and the lattice $LL'$ of subgroups of $G$, normalized by $D$. We say that $LL$ satisfies sandwich classification theorem if $LL$ splits into a disjoint union of sandwiches $L(F,N_G(F))$ over all subgroups $F$ such that the normal closure of $D$ in $F$ coincides with $F$. Here $N_G(F)$ denotes the normalizer of $F$ in $G$. A similar notion of sandwich classification is introduced for the lattice $LL'$. If $D$ is perfect, i.,e. coincides with its commutator subgroup, then it turns out that sandwich classification theorem for $LL$ and $LL'$ are equivalent. We also show how to find basic subroup $F$ of sandwiches for $LL'$ and review sandwich classification theorems in algebraic groups over rings.
http://ijgt.ui.ac.ir/article_10515_09350789c2e261ccde151cedd39968fe.pdf
subgroup structure
sandwich classification
Chevalley groups
commutative rings
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2015-09-01
4
3
13
19
10630
Finite simple groups of low rank: Hurwitz generation and $(2,3)$-generation
Marco Pellegrini
marcoantonio.pellegrini@unicatt.it
1
Maria Tamburini
mariaclara.tamburini@unicatt.it
2
Universita Cattolica del Sacro Cuore
Universita Cattolica del Sacro Cuore
Let us consider the set of non-abelian finite simple groups which admit non-trivial irreducible projective representations of degree $le 7$ over an algebraically closed field $F$ of characteristic $pgeq 0$. We survey some recent results which lead to the complete list of the groups in this set which are $(2, 3, 7)$-generated and of those which are $(2,3)$-generated.
http://ijgt.ui.ac.ir/article_10630_d76e418244e79725ce81061e94048b61.pdf
Finite simple groups
$(2
3)$-generation
Hurwitz generation
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2015-09-01
4
3
21
75
5551
The local nilpotence theorem for 4-Engel groups revisited
Gunnar Traustason
gt223@bath.ac.uk
1
University of Bath
The proof of the local nilpotence theorem for $4$-Engel groups was completed by G. Havas and M. Vaughan-Lee in 2005. The complete proof on the other hand is spread over several articles and the aim of this paper is to give a complete coherent linear version. In the process we are also able to make a few simplifications and in particular we are able to merge two of the key steps into one.
http://ijgt.ui.ac.ir/article_5551_c975d089a43eec9ab751688d5f9df967.pdf
4-Engel
nilpotence
left Engel
eng
University of Isfahan
International Journal of Group Theory
2251-7650
2251-7669
2015-09-01
4
3
77
117
11019
Conjugacy in relatively extra-large Artin groups
Arye Juhasz
arju@tx.technion.ac.il
1
Italy
In this work we consider conjugacy of elements and parabolic subgroups in details, in a new class of Artin groups, introduced in an earlier work, which may contain arbitrary parabolic subgroups. In particular, we find algorithmically minimal representatives of elements in a conjugacy class and also an algorithm to pass from one minimal representative to the others.
http://ijgt.ui.ac.ir/article_11019_6eed0378df31f689d018e18d852b49d7.pdf
Artin groups
Relative presentations
Small cancellation theory
Conjugacy in groups