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Primary Cosets in Groups. / Zhurtov, A. Kh; Lytkina, D. V.; Mazurov, V. D.
в: Algebra and Logic, Том 59, № 3, 07.2020, стр. 216-221.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Primary Cosets in Groups
AU - Zhurtov, A. Kh
AU - Lytkina, D. V.
AU - Mazurov, V. D.
N1 - Publisher Copyright: © 2020, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/7
Y1 - 2020/7
N2 - A finite group G is called a generalized Frobenius group with kernel F if F is a proper nontrivial normal subgroup of G, and for every element Fx of prime order p in the quotient group G/F, the coset Fx of G consists of p-elements. We study generalized Frobenius groups with an insoluble kernel F. It is proved that F has a unique non- Abelian composition factor, and that this factor is isomorphic to L2(32l) for some natural number l. Moreover, we look at a (not necessarily finite) group generated by a coset of some subgroup consisting solely of elements of order three. It is shown that such a group contains a nilpotent normal subgroup of index three.
AB - A finite group G is called a generalized Frobenius group with kernel F if F is a proper nontrivial normal subgroup of G, and for every element Fx of prime order p in the quotient group G/F, the coset Fx of G consists of p-elements. We study generalized Frobenius groups with an insoluble kernel F. It is proved that F has a unique non- Abelian composition factor, and that this factor is isomorphic to L2(32l) for some natural number l. Moreover, we look at a (not necessarily finite) group generated by a coset of some subgroup consisting solely of elements of order three. It is shown that such a group contains a nilpotent normal subgroup of index three.
KW - coset
KW - generalized Frobenius group
KW - insoluble group
KW - projective special linear group
UR - http://www.scopus.com/inward/record.url?scp=85094682730&partnerID=8YFLogxK
U2 - 10.1007/s10469-020-09593-w
DO - 10.1007/s10469-020-09593-w
M3 - Article
AN - SCOPUS:85094682730
VL - 59
SP - 216
EP - 221
JO - Algebra and Logic
JF - Algebra and Logic
SN - 0002-5232
IS - 3
ER -
ID: 25992989