Lifting of generating subgroups

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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.

Original languageEnglish
Pages (from-to)2217-2219
Number of pages3
JournalProceedings of the American Mathematical Society
Issue number8
StatePublished - 1 Jan 1997

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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