Dual-Dedekind subgroups in finite groups

The object of this article is to show that a Jordan-Hölder class structure of a finite group determines abelian Hall subgroups of the group up to isomorphism. The proof uses this classification of the finite simple groups.

Finite groups with few conjugacy classes of subgroups

Rolf Brandl, Libero Verardi (1992)

Rendiconti del Seminario Matematico della Università di Padova

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Finite groups in which $τ$ -quasinormality is a transitive relation

Vladimir O. Lukyanenko, Alexander N. Skiba (2010)

Rendiconti del Seminario Matematico della Università di Padova

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On cover-avoiding subgroups of Sylow subgroups of finite groups

Yangming Li (2010)

Rendiconti del Seminario Matematico della Università di Padova

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Abelian quasinormal subgroups of groups

Stewart E. Stonehewer, Giovanni Zacher (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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Let $G$ be any group and let $A$ be an abelian quasinormal subgroup of $G$ . If $n$ is any positive integer, either odd or divisible by $4$ , then we prove that the subgroup $A^{n}$ is also quasinormal in $G$ .