Let G be a finite group and let C be a subgroup of G. We prove that in order to get information on the set of primes dividing the index |G:C| of C in G it is enough to look at the primes dividing |H:C∩H|, where H is a suitable subgroup of G with few generators.
Recognizing the prime divisors of the index of a proper subgroup
LUCCHINI, ANDREA;
2011
Abstract
Let G be a finite group and let C be a subgroup of G. We prove that in order to get information on the set of primes dividing the index |G:C| of C in G it is enough to look at the primes dividing |H:C∩H|, where H is a suitable subgroup of G with few generators.
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