Geodesic
On new examples of hypocritical groups
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 305-313.

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

A group $ G $ is called hypocritical if whenever $ G $ lies in a locally finite variety generated by a section closed class of groups $ \mathfrak{X} $, then $ G $ belongs to $ \mathfrak{X} $. We prove that some coprime extensions of a $ p $-group are hypocritical. The first example is given when such a $ p $-group is nonabelian.
Keywords: locally finite varieties, finite groups, extraspecial $ p $-groups. 
@article{SEMR_2018_15_a7,
     author = {S. V. Skresanov},
     title = {On new examples of hypocritical groups},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {305--313},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a7/}
}
TY  - JOUR
AU  - S. V. Skresanov
TI  - On new examples of hypocritical groups
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 305
EP  - 313
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a7/
LA  - en
ID  - SEMR_2018_15_a7
ER  - 
%0 Journal Article
%A S. V. Skresanov
%T On new examples of hypocritical groups
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 305-313
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a7/
%G en
%F SEMR_2018_15_a7
S. V. Skresanov. On new examples of hypocritical groups. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 305-313. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a7/

[1] L.F. Harris, “Hypocritical and sincere groups”, Proc. Second Internat. Conf. Theory of Groups, 372 (1973), 333–336 | DOI | MR

[2] L.G. Kovács, M.F. Newman, “Minimal verbal subgroups”, Proc. Camb. Phil. Soc., 62 (1966), 347–350 | DOI | MR

[3] D. Gorenstein, Finite groups, 2nd edition, Chelsea Publishing Co., New York, 1980 | MR

[4] V. D. Mazurov, E. I. Khukhro (eds.), Unsolved problems in group theory. The Kourovka Notebook, 18th edn., Sobolev Institute of Mathematics, Novosibirsk, 2014 | MR

[5] A.V. Vasil'ev, S.V. Skresanov, “On L.G. Kovàcs' problem”, Algebra and Logic, 55:4 (2016), 512–518 | MR

[6] G. Higman, “Some remarks on varieties of groups”, Quart. J. Math. Oxford Ser., 10 (1959), 165–178 | DOI | MR