Let F be a field, A be a vector space over F, GL(F, A) be the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dim F(B/Core G(B)) is finite. In the current article, we study linear groups G such that every subspace of A is either nearly G-invariant or almost G-invariant in the case when G is a soluble p-group where p = char F.
New results on tight connections among pronormal, abnormal and contranormal subgroups of a group have been established. In particular, new characteristics of pronormal and abnormal subgroups have been obtained.
Let F be a field, A be a vector space over F, and GL(F,A) the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dimF(B/CoreG(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF.
This article is dedicated to some criteria of generalized nilpotency involving pronormality and abnormality. Also new results on groups, in which abnormality is a transitive relation, have been obtained.
This article is dedicated to soluble groups, in which pronormality is a transitive relation. Complete description of such groups is obtained.
The article is dedicated to groups in which the set of abnormal and normal subgroups (-subgroups) forms a lattice. A complete description of these groups under the additional restriction that every counternormal subgroup is abnormal is obtained.
A modular analogue of the well-known group theoretical result about finiteness of the derived subgroup in a group with a finite factor by its center has been obtained.
In this paper we obtain the description of the Leibniz algebras whose subalgebras are ideals.
This article discusses the Leibniz algebras whose upper hypercenter has finite codimension. It is proved that such an algebra includes a finite dimensional ideal such that the factor-algebra is hypercentral. This result is an extension to the Leibniz algebra of the corresponding result obtained earlier for Lie algebras. It is also analogous to the corresponding results obtained for groups and modules.
We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras.
2010 Mathematics Subject Classification: Primary 20N25; Secondary 08A72, 03E72.
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