Some Results on p-Nilpotence and Supersolvability of Finite Groups |
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Authors: | M Asaad |
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Institution: | 1. Department of Mathematics, Faculty of Science , Cairo University , Giza, Egypt moasmo45@yahoo.com |
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Abstract: | Let G be a finite group. A subgroup K of a group G is called an ?-subgroup of G if N G (K) ∩ K x ≦ K for all x ? G. The set of all ?-subgroups of G will be denoted by ?(G). Let P be a nontrivial p-group. A chain of subgroups 1 = P 0 ? P 1 ? ··· ? P n = P is called a maximal chain of P provided that |P i : P i?1| = p, i = 1, 2, ···, n. A nontrivial p-subgroup P of G is called weakly supersolvably embedded in G if P has a maximal chain 1 = P 0 ? P 1 ? ··· ? P i ? ··· ? P n = P such that P i ? ?(G) for i = 1, 2, ···, n. Using the concept of weakly supersolvably embedded, we obtain new characterizations of p-nilpotent and supersolvable finite groups. |
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Keywords: | p-nilpotent groups Saturated formations Supersolvable groups |
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