Cyclic quasinormal subgroups of arbitrary groups
Defektschranken gewisser Subnormalteiler.
Erratum to: “Subnormal, permutable, and embedded subgroups in finite groups”
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 in which subnormalizers are subgroups
Finite groups in which -quasinormality is a transitive relation
Finite groups with -subnormal conditions.
Finite groups with subnormal Shmidt subgroups.
Finite Groups with Weakly s-Permutably Embedded and Weakly s-Supplemented Subgroups
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 of G contained in H such that G = HT and ; H is called weakly s-supplemented in G if there is a subgroup T of G such that G = HT and , where 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...
Generalizations of Sylow's theorem.
Gruppen, in denen das Normalteilersein transitiv ist.
Gruppi finiti con molti sottogruppi seminormali
Un sottogruppo di un gruppo è chiamato seminormale se è permutabile con ogni sottogruppo di un conveniente supplemento di in (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 -gruppo finito ( primo dispari) in cui ogni sottogruppo di Sylow è seminormale gode della proprietà che tutti i suoi sottogruppi sono a due a due permutabili.
Gruppi finiti i cui sottogruppi sono o subnormali o pronormali - II
Gruppi finiti i cui sottogruppi sono o subnormali o pronormali
Gruppi finiti risolubili in cui tutti i sottogruppi subnormali hanno difetto al più
Gruppi minimali non in
Kriterien für Subnormalität in endlichen Gruppen.
Lokale Subnormalteiler und ihr nilpotentes Residuum.
Maximal subgroups and PST-groups
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...
Normality Conditions for Quasinormal Subgroups in Finite Groups.
On a class of finite solvable groups
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...