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.
ASJC Scopus subject areas
- Applied Mathematics