Lifting of generating subgroups

Ido Efrat

doi:10.1090/s0002-9939-97-03917-8

Lifting of generating subgroups

Ido Efrat

Department of Mathematics

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

1 Scopus citations

Abstract

Let ψ G → H be an epimorphism of finite groups. Suppose that G is generated by its subgroups G₁,... ,G_n and that H is generated by its subgroups H₁,... ,H_n- Furthermore, suppose that f(Gi) and Hi are conjugate, i = 1,... ,n. We prove that there exist g₁,... ,g_n G G such that G₁^g1,... ,G_n^gn generate G and ψ(G_i^gi) = H_i, i = 1,... ,n.

Original language	English
Pages (from-to)	2217-2219
Number of pages	3
Journal	Proceedings of the American Mathematical Society
Volume	125
Issue number	8
DOIs	https://doi.org/10.1090/s0002-9939-97-03917-8
State	Published - 1 Jan 1997

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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title = "Lifting of generating subgroups",

abstract = "Let ψ G → H be an epimorphism of finite groups. Suppose that G is generated by its subgroups G1,... ,Gn and that H is generated by its subgroups H1,... ,Hn- Furthermore, suppose that f(Gi) and Hi are conjugate, i = 1,... ,n. We prove that there exist g1,... ,gn G G such that G1g1,... ,Gngn generate G and ψ(Gigi) = Hi, i = 1,... ,n.",

author = "Ido Efrat",

year = "1997",

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PY - 1997/1/1

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N2 - Let ψ G → H be an epimorphism of finite groups. Suppose that G is generated by its subgroups G1,... ,Gn and that H is generated by its subgroups H1,... ,Hn- Furthermore, suppose that f(Gi) and Hi are conjugate, i = 1,... ,n. We prove that there exist g1,... ,gn G G such that G1g1,... ,Gngn generate G and ψ(Gigi) = Hi, i = 1,... ,n.

AB - Let ψ G → H be an epimorphism of finite groups. Suppose that G is generated by its subgroups G1,... ,Gn and that H is generated by its subgroups H1,... ,Hn- Furthermore, suppose that f(Gi) and Hi are conjugate, i = 1,... ,n. We prove that there exist g1,... ,gn G G such that G1g1,... ,Gngn generate G and ψ(Gigi) = Hi, i = 1,... ,n.

UR - https://www.scopus.com/pages/publications/33646966647

U2 - 10.1090/s0002-9939-97-03917-8

DO - 10.1090/s0002-9939-97-03917-8

M3 - Article

AN - SCOPUS:33646966647

SN - 0002-9939

VL - 125

SP - 2217

EP - 2219

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 8

ER -

Lifting of generating subgroups

Abstract

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