Geodesic
Perfectly stable and normal subgroups
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 56 (2022) no. 1, pp. 27-32.

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

The equivalence between the concepts of normal and perfectly stable subgroups is shown. The proof of the main theorem is based on a novel concept of hypergroups over a group.
Keywords: hypergroup over a group, perfectly stable, normal subgroups. 
@article{UZERU_2022_56_1_a3,
     author = {Sh. K. Navasardyan},
     title = {Perfectly stable and normal subgroups},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {27--32},
     publisher = {mathdoc},
     volume = {56},
     number = {1},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2022_56_1_a3/}
}
TY  - JOUR
AU  - Sh. K. Navasardyan
TI  - Perfectly stable and normal subgroups
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2022
SP  - 27
EP  - 32
VL  - 56
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2022_56_1_a3/
LA  - en
ID  - UZERU_2022_56_1_a3
ER  - 
%0 Journal Article
%A Sh. K. Navasardyan
%T Perfectly stable and normal subgroups
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2022
%P 27-32
%V 56
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2022_56_1_a3/
%G en
%F UZERU_2022_56_1_a3
Sh. K. Navasardyan. Perfectly stable and normal subgroups. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 56 (2022) no. 1, pp. 27-32. http://geodesic.mathdoc.fr/item/UZERU_2022_56_1_a3/

[1] R. Lal, R. P. Shukla, “Perfectly Stable Subgroups of Finite Groups”, Communications in Algebra, 24 (1996), 643–657 | DOI | MR | Zbl

[2] R. Baer, “Nets and Groups.”, Trans. Amer. Math. Soc., 46 (1939), 110–141 | DOI | MR | Zbl

[3] R. Lal, “Transversals in Groups”, Journal of Algebra, 181 (1996), 70–81 | DOI | MR | Zbl

[4] M. Niemenmaa, T. Kepka, “On Multiplication Groups of Loops”, J. of Algebra, 135 (1990), 112–122 | DOI | MR | Zbl

[5] M. Niemenmaa, M. Rytty, “Connected Transversals and Multiplication Groups of Loops”, Quasigroups and Related Systems, 15 (2007), 95–107 | MR | Zbl

[6] S. Dalalyan, “Equivalence of the Categories of Group Triples and of Hypergroups over the Group”, arXiv: 1908.01360 | DOI

[7] S. Dalalyan, Sh. Navasardyan, “On Unitary Hypergroups over the Group”, Lobachevskii Journal of Mathematics, 40 (2019), 1045–1057 | DOI | MR | Zbl

[8] R. Lal, R. P. Shukla, “Characterization of Tarski Monsters”, Indian Journal of Pure and Applied Mathematics, 36 (2005), 2321–2327 | MR

[9] R. Lal, R. P. Shukla, “Transversals in Non-discrete Groups”, Proceedings Mathematical Sciences, 115 (2006) | DOI | MR | Zbl

[10] S. H. Dalalyan, Hypergroups over the Group and Generalizations of \uppercase{S}chreier's Theorem on Group Extensions, 2014, arXiv: 1403.6134v1 | DOI | Zbl

[11] J. J. Rotman, “An Introduction to the Theory of Groups”, Springer Science Business Media, 148 (2012) | MR

[12] Sh. Navasardyan, “Independence of the Axioms of Hypergroup over the Group”, Armenian Journal of Mathematics, 13 (2021), 1–11 | DOI | MR