A note on groups with many locally supersoluble subgroups
Francesco
de Giovanni
Dipartimento di Matematica e Applicazioni - University of Napoli Federico II
author
Marco
Trombetti
Dipartimento di Matematica e Applicazioni - University of Napoli Federico II
author
text
article
2015
eng
It is proved here that if $G$ is a locally graded group satisfying the minimal condition on subgroups which are not locally supersoluble, then $G$ is either locally supersoluble or a Cernikov group. The same conclusion holds for locally finite groups satisfying the weak minimal condition on non-(locally supersoluble) subgroups. As a consequence, it is shown that any infinite locally graded group whose non-(locally supersoluble) subgroups lie into finitely many conjugacy classes must be locally supersoluble.
International Journal of Group Theory
University of Isfahan
2251-7650
4
v.
2
no.
2015
1
7
http://ijgt.ui.ac.ir/article_9144_9334581bb870e89c7b3b96752c3d4ee3.pdf
dx.doi.org/10.22108/ijgt.2015.9144
On residually finite semigroups of cellullar automata
Tullio
Ceccherini-Silberstein
Dipartimento di Ingegneria, Università del Sannio
author
Michel
Coornaert
IRMA
author
text
article
2015
eng
We prove that if $M$ is a monoid and $A$ a finite set with more than one element, then the residual finiteness of $M$ is equivalent to that of the monoid consisting of all cellular automata over $M$ with alphabet $A$.
International Journal of Group Theory
University of Isfahan
2251-7650
4
v.
2
no.
2015
9
15
http://ijgt.ui.ac.ir/article_9371_d9d2ea9f8888eea71e9b2c32637ec037.pdf
dx.doi.org/10.22108/ijgt.2015.9371
On soluble groups whose subnormal subgroups are inert
Ulderico
Dardano
Dipartimento Matematica e Appl., v. Cintia, M.S.Angelo 5a,
I-80126 Napoli (Italy)
author
Silvana
Rinauro
Dipartimento di Matematica, Informatica ed Economia, Universita della Basilicata,
Viale dell'Ateneo Lucano 10, I-85100
author
text
article
2015
eng
A subgroup H of a group G is called inert if, for each $g\in G$, the index of $H\cap H^g$ in $H$ is finite. We give a classification of soluble-by-finite groups $G$ in which subnormal subgroups are inert in the cases where $G$ has no nontrivial torsion normal subgroups or $G$ is finitely generated.
International Journal of Group Theory
University of Isfahan
2251-7650
4
v.
2
no.
2015
17
24
http://ijgt.ui.ac.ir/article_9373_1b5f405a32618ca02d6d467026ade139.pdf
dx.doi.org/10.22108/ijgt.2015.9373
On double cosets with the trivial intersection property and Kazhdan-Lusztig cells in $S_n$
Thomas P.
McDonough
Department of Mathematics, Aberystwyth University
author
Christos A.
Pallikaros
Department of Mathematics and Statistics, University of Cyprus
author
text
article
2015
eng
For a composition $\lambda$ of $n$ our aim is to obtain reduced forms for all the elements in the $w_{J(\lambda)}$, the longest element of the standard parabolic subgroup of $S_n$ corresponding to $\lambda$. We investigate how far this is possible to achieve by looking at elements of the form $w_{J(\lambda)}d$, where $d$ is a prefix of an element of minimum length in a $(W_{J(\lambda)},B)$ double coset with the trivial intersection property, $B$ being a parabolic subgroup of $S_n$ whose type is `dual' to that of $W_{J(\lambda)}$.
International Journal of Group Theory
University of Isfahan
2251-7650
4
v.
2
no.
2015
25
48
http://ijgt.ui.ac.ir/article_9795_baa13d009c9d26331351ea54f83b545d.pdf
dx.doi.org/10.22108/ijgt.2015.9795
Bias of group generators in finite and profinite groups: known results and open problems
Eleonora
Crestani
Dipartimento di Matematica
Universita; di Padova
author
Andrea
Lucchini
Dipartimento di Matematica
Universita; di Padova
author
text
article
2015
eng
We analyze some properties of the distribution $Q_{G,k}$ of the first component in a $k$-tuple chosen uniformly in the set of all the $k$-tuples generating a finite group $G$ (the limiting distribution of the product replacement algorithm). In particular, we concentrate our attention on the study of the variation distance $\beta_k(G)$ between $Q_{G,k}$ and the uniform distribution. We review some known results, analyze several examples and propose some intriguing open questions.
International Journal of Group Theory
University of Isfahan
2251-7650
4
v.
2
no.
2015
49
67
http://ijgt.ui.ac.ir/article_9895_88e6083ca4021d45413514f530fff685.pdf
dx.doi.org/10.22108/ijgt.2015.9895
Conjugate factorizations of finite groups
Martino
Garonzi
University of Brasilia
author
text
article
2015
eng
In this paper we illustrate recent results about factorizations of finite groups into conjugate subgroups. The illustrated results are joint works with John Cannon, Dan Levy, Attila Mar\'oti and Iulian I. Simion.
International Journal of Group Theory
University of Isfahan
2251-7650
4
v.
2
no.
2015
69
78
http://ijgt.ui.ac.ir/article_9931_e6b6bd290603e46326f526f336cb5c6f.pdf
dx.doi.org/10.22108/ijgt.2015.9931