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Finite $p$ -nilpotent groups with some subgroups weakly $ℳ$ -supplemented

Liushuan Dong (2020)

Czechoslovak Mathematical Journal

Suppose that $G$ is a finite group and $H$ is a subgroup of $G$ . Subgroup $H$ is said to be weakly $ℳ$ -supplemented in $G$ if there exists a subgroup $B$ of $G$ such that (1) $G = H B$ , and (2) if $H_{1} / H_{G}$ is a maximal subgroup of $H / H_{G}$ , then $H_{1} B = B H_{1} < G$ , where $H_{G}$ is the largest normal subgroup of $G$ contained in $H$ . We fix in every noncyclic Sylow subgroup $P$ of $G$ a subgroup $D$ satisfying $1 < | D | < | P |$ and study the $p$ -nilpotency of $G$ under the assumption that every subgroup $H$ of $P$ with $| H | = | D |$ is weakly $ℳ$ -supplemented in $G$ . Some recent results are generalized.

Displaying 21 – 32 of 32

Finite $p$ -nilpotent groups with some subgroups weakly $ℳ$ -supplemented

Finite p'-nilpotent groups. I.

Finite soluble and nilpotent groups with a restriction on the rank of the centralizer of an automorphism of prime order.

Fischer classes in finite groups.

Fitting Formations of finite Soluble Groups.

Fitting height of $A$ -nilpotent groups

Fittingfunktoren in endlichen auflösbaren Gruppen. I.

Fixed point free action with regular orbits.

Fonction de Möbius d'un groupe fini et anneau de Burnside.

Formations generated by a group of socle length 2.

Frattini theory for classes of finite universal algebras of Mal'tsev varieties.

Frobenius Subgroups of Free Products of Prosolvable Groups.

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