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Erratum to: “Subnormal, permutable, and embedded subgroups in finite groups”

James Beidleman, Mathew Ragland (2012)

Open Mathematics

The original version of the article was published in Central European Journal of Mathematics, 2011, 9(4), 915–921, DOI: 10.2478/s11533-011-0029-8. Unfortunately, the original version of this article contains a mistake: Lemma 2.1 (2) is not true. We correct Lemma 2.2 (2) and Theorem 1.1 in our paper where this lemma was used.

Finite Groups with Weakly s-Permutably Embedded and Weakly s-Supplemented Subgroups

Changwen Li (2011)

Bulletin of the Polish Academy of Sciences. Mathematics

Suppose G is a finite group and H is a subgroup of G. H is called weakly s-permutably embedded in G if there are a subnormal subgroup T of G and an s-permutably embedded subgroup H s e of G contained in H such that G = HT and H T H s e ; H is called weakly s-supplemented in G if there is a subgroup T of G such that G = HT and H T H s G , where H s G is the subgroup of H generated by all those subgroups of H which are s-permutable in G. We investigate the influence of the existence of s-permutably embedded and weakly s-supplemented...

Gruppi finiti con molti sottogruppi seminormali

Guido Zappa (1993)

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

Un sottogruppo S di un gruppo G è chiamato seminormale se è permutabile con ogni sottogruppo di un conveniente supplemento di S in G (X. SU [2]). Nel nostro lavoro vengono caratterizzati tutti i gruppi finiti in cui ogni sottogruppo di Sylow è seminormale. Viene anche dimostrato che ogni p -gruppo finito ( p primo dispari) in cui ogni sottogruppo di Sylow è seminormale gode della proprietà che tutti i suoi sottogruppi sono a due a due permutabili.

Maximal subgroups and PST-groups

Adolfo Ballester-Bolinches, James Beidleman, Ramón Esteban-Romero, Vicent Pérez-Calabuig (2013)

Open Mathematics

A subgroup H of a group G is said to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable...

On a class of finite solvable groups

James Beidleman, Hermann Heineken, Jack Schmidt (2013)

Open Mathematics

A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on L as a group...

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