227-01227-01227-01-property and normal subgroups |
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Authors: | Anna Luisa Gilotti |
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Affiliation: | (1) Present address: Istituto di Matematica Applioata «G. Sansone», Università degli Studi di Firenze, Via di S. Marta 3, 50139 Firenze, Italia |
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Abstract: | Summary D-property (=set of primes) in finite groups is not in general inherited by subgroups. In this paper, as evidence in favor of the following conjecture (F. Gross): (o) If a finite group G satisfies D then its normal subgroups satisfy D-property as well. the Author shows that if the D and the D-properties (=set of the primes not in ) hold together in a finite group G, then both are inherited by the normal subgroups of G. As a corollary, the characterization of the groups satisfying both the properties D and D is given in terms of the composition factors. |
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