On Groups Whose Small-Order Elements Generate a Small Subgroup
Matematičeskie zametki, Tome 92 (2012) no. 3, pp. 361-367.

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

It is proved that every finite group $G$ can be represented as the quotient group of some finite group $K$ such that all elements of “small” primary orders in $K$ generate an Abelian normal subgroup.
Keywords: finite group, primary order, Abelian group, cohomology of a group, Abelian $p$-group, exponent of a group.
Mots-clés : solvable group
@article{MZM_2012_92_3_a3,
     author = {V. P. Burichenko},
     title = {On {Groups} {Whose} {Small-Order} {Elements} {Generate} a {Small} {Subgroup}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {361--367},
     publisher = {mathdoc},
     volume = {92},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_92_3_a3/}
}
TY  - JOUR
AU  - V. P. Burichenko
TI  - On Groups Whose Small-Order Elements Generate a Small Subgroup
JO  - Matematičeskie zametki
PY  - 2012
SP  - 361
EP  - 367
VL  - 92
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_92_3_a3/
LA  - ru
ID  - MZM_2012_92_3_a3
ER  - 
%0 Journal Article
%A V. P. Burichenko
%T On Groups Whose Small-Order Elements Generate a Small Subgroup
%J Matematičeskie zametki
%D 2012
%P 361-367
%V 92
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2012_92_3_a3/
%G ru
%F MZM_2012_92_3_a3
V. P. Burichenko. On Groups Whose Small-Order Elements Generate a Small Subgroup. Matematičeskie zametki, Tome 92 (2012) no. 3, pp. 361-367. http://geodesic.mathdoc.fr/item/MZM_2012_92_3_a3/

[1] Y. Berkovich, L. Kazarin, “Indices of elements and normal structure of finite groups”, J. Algebra, 283:2 (2005), 564–583 | DOI | MR | Zbl

[2] V. N. Tyutyanov, “Konechnye gruppy, u kotorykh vse elementy prostykh poryadkov soderzhatsya v podgruppe Frattini”, Izv. Gomelsk. gos. un-ta im. F. Skoriny, 41:2 (2007), 59–61

[3] Nereshennye voprosy teorii grupp. Kourovskaya tetrad, 17-e izd., eds. V. D. Mazurov, E. I. Khukhro, In-t matem. SO RAN, Novosibirsk, 2010

[4] K. S. Braun, Kogomologii grupp, Nauka, M., 1987 | MR | Zbl

[5] C. Maklein, Gomologiya, Mir, M., 1966 | MR | Zbl