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Primary Cosets in Groups. / Zhurtov, A. Kh; Lytkina, D. V.; Mazurov, V. D.

In: Algebra and Logic, Vol. 59, No. 3, 07.2020, p. 216-221.

Research output: Contribution to journal › Article › peer-review

Harvard

Zhurtov, AK, Lytkina, DV & Mazurov, VD 2020, 'Primary Cosets in Groups', Algebra and Logic, vol. 59, no. 3, pp. 216-221. https://doi.org/10.1007/s10469-020-09593-w

APA

Zhurtov, A. K., Lytkina, D. V., & Mazurov, V. D. (2020). Primary Cosets in Groups. Algebra and Logic, 59(3), 216-221. https://doi.org/10.1007/s10469-020-09593-w

Vancouver

Zhurtov AK, Lytkina DV , Mazurov VD. Primary Cosets in Groups. Algebra and Logic. 2020 Jul;59(3):216-221. doi: 10.1007/s10469-020-09593-w

Author

Zhurtov, A. Kh ; Lytkina, D. V. ; Mazurov, V. D. / Primary Cosets in Groups. In: Algebra and Logic. 2020 ; Vol. 59, No. 3. pp. 216-221.

BibTeX

@article{f64f28496dde4dc181ba4520f60c6032,

title = "Primary Cosets in Groups",

abstract = "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.",

keywords = "coset, generalized Frobenius group, insoluble group, projective special linear group",

author = "Zhurtov, {A. Kh} and Lytkina, {D. V.} and Mazurov, {V. D.}",

year = "2020",

month = jul,

doi = "10.1007/s10469-020-09593-w",

language = "English",

volume = "59",

pages = "216--221",

journal = "Algebra and Logic",

issn = "0002-5232",

publisher = "Springer US",

number = "3",

}

RIS

TY - JOUR

T1 - Primary Cosets in Groups

AU - Zhurtov, A. Kh

AU - Lytkina, D. V.

AU - Mazurov, V. D.

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