Eine Verallgemeinerung des Regularitätsbegriffes bei p-Gruppen I
Elementary Abelian operator groups.
Every -group with all subgroups normal-by-finite is locally finite
A group has all of its subgroups normal-by-finite if is finite for all subgroups of . The Tarski-groups provide examples of -groups ( a “large” prime) of nonlocally finite groups in which every subgroup is normal-by-finite. The aim of this paper is to prove that a -group with every subgroup normal-by-finite is locally finite. We also prove that if for every subgroup of , then contains an Abelian subgroup of index at most .
Existentially closed -groups
Finitely generated soluble groups with an Engel condition on infinite subsets
Galois theory for groups
Group algebras with centrally metabelian unit groups.
Given a field K of characteristic p > 2 and a finite group G, necessary and sufficient conditions for the unit group U(KG) of the group algebra KG to be centrally metabelian are obtained. It is observed that U(KG) is centrally metabelian if and only if KG is Lie centrally metabelian.
Groups in which the derived groups of all 2-generator subgroups are cyclic
Groups whose all subgroups are ascendant or self-normalizing
This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which of course are ascendant [Stonehewer S.E., Permutable subgroups of infinite groups, Math. Z., 1972,...
Groups with complete lattice of nearly normal subgroups.
A subgroup H of a group G is said to be nearly normal in G if it has finite index in its normal closure in G. A well-known theorem of B.H. Neumann states that every subgroup of a group G is nearly normal if and only if the commutator subgroup G' is finite. In this article, groups in which the intersection and the join of each system of nearly normal subgroups are likewise nearly normal are considered, and some sufficient conditions for such groups to be finite-by-abelian are given.
Groups with Restricted Conjugacy Classes
Let F C 0 be the class of all finite groups, and for each nonnegative integer n define by induction the group class FC^(n+1) consisting of all groups G such that for every element x the factor group G/CG ( <x>^G ) has the property FC^n . Thus FC^1 -groups are precisely groups with finite conjugacy classes, and the class FC^n obviously contains all finite groups and all nilpotent groups with class at most n. In this paper the known theory of FC-groups is taken as a model, and it is shown that...
Groups with Restricted Non-Normal Subgroups.
Groups with soluble factor groups and projectivities
Groups with subnormal subgroups of bounded defect
Homological and Topological Properties of Locally Indicable Groups.
Homology and derived series of groups.
Homotopy Lie algebras; lower central series and the Koszul property.
Hyper–(Abelian–by–finite) groups with many subgroups of finite depth
The main result of this note is that a finitely generated hyper-(Abelian-by-finite) group is finite-by-nilpotent if and only if every infinite subset contains two distinct elements , such that
Isomorphism classes and derived series of certain almost-free groups.
Just-non-SRI*-groups