Minimal Involution-Free Nongroup Reduced Twisted Subsets
Matematičeskie zametki, Tome 88 (2010) no. 6, pp. 902-910.

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

A subset $K$ of a group $G$ is said to be twisted if $1\in K$ and the element $xy^{-1}x$ lies in $K$ for any $x,y\in K$. We study finite involution-free twisted subsets that are not subgroups but all of whose proper twisted subsets are subgroups.
Mots-clés : group
Keywords: subgroup, twisted subset, involution-free subset.
@article{MZM_2010_88_6_a9,
     author = {A. L. Myl'nikov},
     title = {Minimal {Involution-Free} {Nongroup} {Reduced} {Twisted} {Subsets}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {902--910},
     publisher = {mathdoc},
     volume = {88},
     number = {6},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_6_a9/}
}
TY  - JOUR
AU  - A. L. Myl'nikov
TI  - Minimal Involution-Free Nongroup Reduced Twisted Subsets
JO  - Matematičeskie zametki
PY  - 2010
SP  - 902
EP  - 910
VL  - 88
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2010_88_6_a9/
LA  - ru
ID  - MZM_2010_88_6_a9
ER  - 
%0 Journal Article
%A A. L. Myl'nikov
%T Minimal Involution-Free Nongroup Reduced Twisted Subsets
%J Matematičeskie zametki
%D 2010
%P 902-910
%V 88
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2010_88_6_a9/
%G ru
%F MZM_2010_88_6_a9
A. L. Myl'nikov. Minimal Involution-Free Nongroup Reduced Twisted Subsets. Matematičeskie zametki, Tome 88 (2010) no. 6, pp. 902-910. http://geodesic.mathdoc.fr/item/MZM_2010_88_6_a9/

[1] A. L. Mylnikov, “Konechnye perekruchennye gruppy”, Sib. matem. zhurn., 48:2 (2007), 369–375 | MR | Zbl

[2] M. Aschbacher, “Near subgroups of finite groups”, J. Group Theory, 1:2 (1998), 113–129 | DOI | MR | Zbl

[3] A. L. Mylnikov, “Minimalnye negruppovye skruchennye podmnozhestva, soderzhaschie involyutsiyu”, Algebra i logika, 46:4 (2007), 459–482 | MR | Zbl

[4] A. L. Mylnikov, “Nilpotentnost kommutanta konechnoi perekruchennoi gruppy”, Sib. matem. zhurn., 47:5 (2006), 1117–1127 | MR | Zbl

[5] A. L. Mylnikov, “Konechnye minimalnye neperekruchennye gruppy”, Vestn. Krasnoyarsk. gos. un-ta, 1 (2005), 71–76

[6] A. L. Mylnikov, “O konechnykh minimalnykh neperekruchennykh gruppakh”, Vestn. Krasnoyarsk. gos. un-ta, 4 (2005), 164–169

[7] V. V. Belyaev, A. L. Mylnikov, “Otsenka poryadka gruppy, porozhdennoi konechnym skruchennym podmnozhestvom”, Sib. matem. zhurn., 49:6 (2008), 1235–1237 | MR

[8] D. V. Veprintsev, A. L. Mylnikov, “Involyutivnaya dekompozitsiya gruppy i skruchennye podmnozhestva s malym kolichestvom involyutsii”, Sib. matem. zhurn., 49:2 (2008), 274–279 | MR | Zbl

[9] A. L. Mylnikov, “Abelevy perekruchennye gruppy”, Matem. sistemy, 3, Krasnoyarsk. gos. agrar. un-t, Krasnoyarsk, 2005, 59–61

[10] D. Gorenstein, Finite Groups, Harper Row Publ., New York, 1968 | MR | Zbl

[11] W. Feit, J. G. Thompson, “Solvability of groups of odd order”, Pacific J. Math., 13:3 (1963), 775–1029 | MR | Zbl