TY - JOUR
T1 - Lifting in Frattini covers and a characterization of finite solvable groups
AU - Guralnick, Robert M.
AU - Tiep, Pham Huu
N1 - Publisher Copyright:
© 2015 by De Gruyter.
PY - 2015/11
Y1 - 2015/11
N2 - 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.
AB - 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.
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U2 - 10.1515/crelle-2013-0085
DO - 10.1515/crelle-2013-0085
M3 - Article
AN - SCOPUS:84946844297
SN - 0075-4102
VL - 2015
SP - 49
EP - 72
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 708
ER -