Groups in Which Commutativity Is a Transitive Relation
نویسندگان
چکیده
منابع مشابه
Groups in Which Commutativity Is a Transitive Relation
We investigate the structure of groups in which commutativity is a transitive relation on non-identity elements (CT-groups). A detailed study of locally nite, polycyclic, and torsion-free solvable CT-groups is carried out. Other topics include xed-point-free groups of automorphisms of abelian tor-sion groups and their cohomology groups.
متن کاملON FINITE GROUPS IN WHICH SS-SEMIPERMUTABILITY IS A TRANSITIVE RELATION
Let H be a subgroup of a finite group G. We say that H is SS-semipermutable in Gif H has a supplement K in G such that H permutes with every Sylow subgroup X of Kwith (jXj; jHj) = 1. In this paper, the Structure of SS-semipermutable subgroups, and finitegroups in which SS-semipermutability is a transitive relation are described. It is shown thata finite solvable group G is a PST-group if and on...
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a subgroup x of a group g is said to be an h -subgroup if n_g(x) ∩ x^g ≤ x for each element g belonging to g. in [m. bianchi e. a., on finite soluble groups in which normality is a transitive relation, j. group theory, 3 (2000), 147–156] the authors showed that finite groups in which every subgroup has the h -property are exactly soluble groups in which normality is a transitive relation. here ...
متن کاملGroups in which the Bounded Nilpotency of Two-generator Subgroups is a Transitive Relation
In this paper we describe the structure of locally finite groups in which the bounded nilpotency of two-generator subgroups is a transitive relation. We also introduce the notion of (nilpotent of class c)-transitive kernel. Our results generalize several known results related to the groups in which commutativity is a transitive relation. MSC 2000: 20E15, 20D25
متن کاملPermutations Which Make Transitive Groups Primitive
In this article we look into characterizing primitive groups in the following way. Given a primitive group we single out a subset of its generators such that these generators alone (the so-called primitive generators) imply the group is primitive. The remaining generators ensure transitivity or comply with specific features of the group. We show that, other than the symmetric and alternating gr...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1998
ISSN: 0021-8693
DOI: 10.1006/jabr.1998.7468