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Zbl 0830.20034
Finite groups with normal subgroups of prime power orders.
(English)
[J] PU.M.A., Pure Math. Appl. 5, No. 3, 251-256 (1994). ISSN 1218-4586

Let $G$ be a finite group and if $P$ is a $p$-subgroup of $G$, let $\Omega(P)=\Omega_1(P)$ for $p\ne 2$ ($=\Omega_2(P)$ for $p=2$). The authors' main objective is to study how the condition that all members of the family $\{H\leq\Omega(P)\mid H'=1,\ \text{exp}(H)=p^e\}$ are normal in $G$ influences the structure of $G$. This condition is combined with others in order to derive the supersolvability of $G$ or the $p$-nilpotency of $G$.
[M.Deaconescu (Safat)]
MSC 2000:
*20D10 Solvable finite groups
20D20 Sylow subgroups of finite groups

Keywords: minimal subgroups; supersolvable groups; normal $p$-complements; finite groups; $p$-nilpotency

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