Lifting in Frattini covers and a characterization of finite solvable groups

Robert M. Guralnick, Pham Huu Tiep

Research output: Contribution to journalArticle

10 Scopus citations


We prove a lifting theorem for odd Frattini covers of finite groups. Using this, we generalize a result of J. G. Thompson and characterize finite solvable groups as those finite groups which do not contain nontrivial elements xi, i = 1,2,3, with x1x2x3 = 1 and xi a pi-element for distinct primes pi. We note some connections with coverings of curves.

Original languageEnglish (US)
Pages (from-to)49-72
Number of pages24
JournalJournal fur die Reine und Angewandte Mathematik
Issue number708
Publication statusPublished - Nov 1 2015


ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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