Geodesic
Primary cosets in groups
Algebra i logika, Tome 59 (2020) no. 3, pp. 315-322

Voir la notice de l'article provenant de la source Math-Net.Ru

A finite group $G$ is called a generalized Frobenius group with kernel $F$ if $F$ is a proper nontrivial normal subgroup of $G$, and for every element $Fx$ of prime order $p$ in the quotient group $G/F$, the coset $Fx$ of $G$ consists of $p$-elements. We study generalized Frobenius groups with an insoluble kernel $F$. It is proved that $F$ has a unique non-Abelian composition factor, and that this factor is isomorphic to $L_2(3^{2^l})$ for some natural number $l$. Moreover, we look at a (not necessarily finite) group generated by a coset of some subgroup consisting solely of elements of order three. It is shown that such a group contains a nilpotent normal subgroup of index three.
Keywords: generalized Frobenius group, projective special linear group, coset.
Mots-clés : insoluble group 
@article{AL_2020_59_3_a2,
     author = {A. Kh. Zhurtov and D. V. Lytkina and V. D. Mazurov},
     title = {Primary cosets in groups},
     journal = {Algebra i logika},
     pages = {315--322},
     publisher = {mathdoc},
     volume = {59},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2020_59_3_a2/}
}
TY  - JOUR
AU  - A. Kh. Zhurtov
AU  - D. V. Lytkina
AU  - V. D. Mazurov
TI  - Primary cosets in groups
JO  - Algebra i logika
PY  - 2020
SP  - 315
EP  - 322
VL  - 59
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2020_59_3_a2/
LA  - ru
ID  - AL_2020_59_3_a2
ER  - 
%0 Journal Article
%A A. Kh. Zhurtov
%A D. V. Lytkina
%A V. D. Mazurov
%T Primary cosets in groups
%J Algebra i logika
%D 2020
%P 315-322
%V 59
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2020_59_3_a2/
%G ru
%F AL_2020_59_3_a2
A. Kh. Zhurtov; D. V. Lytkina; V. D. Mazurov. Primary cosets in groups. Algebra i logika, Tome 59 (2020) no. 3, pp. 315-322. http://geodesic.mathdoc.fr/item/AL_2020_59_3_a2/