Geodesic
On the structure of some groups having finite contranormal subgroups
Algebra and discrete mathematics, Tome 31 (2021) no. 1, pp. 109-119 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Following J. S. Rose, a subgroup $H$ of the group $G$ is said to be contranormal in $G$, if $G=H^{G}$. In a certain sense, contranormal subgroups are antipodes to subnormal subgroups. We study the structure of Abelian-by-nilpotent groups having a finite proper contranormal $p$-subgroup.
Keywords: contranormal subgroups, Abelian-by-nilpotent groups, hypercenter of a group, $G$-eccentric subgroups, rationally irreducible subgroups. 
@article{ADM_2021_31_1_a6,
     author = {L. A. Kurdachenko and N. N. Semko},
     title = {On the structure of some groups having finite contranormal subgroups},
     journal = {Algebra and discrete mathematics},
     pages = {109--119},
     year = {2021},
     volume = {31},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2021_31_1_a6/}
}
TY  - JOUR
AU  - L. A. Kurdachenko
AU  - N. N. Semko
TI  - On the structure of some groups having finite contranormal subgroups
JO  - Algebra and discrete mathematics
PY  - 2021
SP  - 109
EP  - 119
VL  - 31
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ADM_2021_31_1_a6/
LA  - en
ID  - ADM_2021_31_1_a6
ER  - 
%0 Journal Article
%A L. A. Kurdachenko
%A N. N. Semko
%T On the structure of some groups having finite contranormal subgroups
%J Algebra and discrete mathematics
%D 2021
%P 109-119
%V 31
%N 1
%U http://geodesic.mathdoc.fr/item/ADM_2021_31_1_a6/
%G en
%F ADM_2021_31_1_a6
L. A. Kurdachenko; N. N. Semko. On the structure of some groups having finite contranormal subgroups. Algebra and discrete mathematics, Tome 31 (2021) no. 1, pp. 109-119. http://geodesic.mathdoc.fr/item/ADM_2021_31_1_a6/

[1] G. Baumslag, “Wreath products and $p$-groups”, Math. Proc. Cambridge Philos. Soc., 55:3 (1959), 224–231 | DOI | MR | Zbl

[2] S.N. Chernikov, The Groups With Prescribed Properties of Systems of Subgroups, Nauka, Moscow, 1980 | MR

[3] M.R. Dixon, Sylow Theory, Formations and Fitting Classes in Locally Finite Groups, World Scientific, Singapore, 1994 | MR | Zbl

[4] M.R. Dixon, L.A. Kurdachenko, I.Ya. Subbotin, Ranks of Groups. The Tools, Characteristics and Restrictions, Wiley, New York, 2017 | MR | Zbl

[5] L. Fuchs, Infinite Abelian Groups, I, Academic Press, New York, 1970 | MR | Zbl

[6] L. A. Kurdachenko, P. Longobardi, M. Maj, On the structure of some locally nilpotent groups without contranormal subgroups, 2020, arXiv: 2006.02345v1 [math.GR] | MR

[7] L. A. Kurdachenko, J. Otal, “The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group”, Centr. Eur. J. Math., 11:10 (2013), 1732–1741 | MR | Zbl

[8] L. A. Kurdachenko, J. Otal, I. Ya. Subbotin, Artinian modules over group rings, Frontiers in Mathematics, Birkhäuser, Basel, 2007 | MR | Zbl

[9] J. S. Rose, “Nilpotent subgroups of finite soluble groups”, Math. Z., 106:2 (1968), 97–112 | DOI | MR | Zbl