The Lattice of Fully Invariant Subgroups of a Cotorsion Group

2021 ◽  
Author(s):  
T. G. Kemoklidze
Keyword(s):  
Fully Invariant Subgroups

scholarly journals On fully invariant subgroups of primary abelian groups.

1976 ◽  
Vol 22 (3) ◽  
pp. 281-284 ◽  
Author(s):  
Ronald C. Linton
Keyword(s):  
Abelian Groups ◽  
Fully Invariant Subgroups

scholarly journals A solution of a problem of Plotkin and Vovsi and an application to varieties of groups

1999 ◽  
Vol 67 (3) ◽  
pp. 329-355 ◽  
Author(s):  
C. K. Gupta ◽  
A. N. Krasil'nikov
Keyword(s):  
Free Group ◽  
Invariant Subgroup ◽  
Arbitrary Field ◽  
Finitely Based ◽  
Maximal Condition ◽  
Infinite Rank ◽  
Characteristic 2 ◽  
Countably Infinite ◽  
Fully Invariant Subgroups ◽  
Relatively Free Group

AbstractLet K be an arbitrary field of characteristic 2, F a free group of countably infinite rank. We construct a finitely generated fully invariant subgroup U in F such that the relatively free group F/U satisfies the maximal condition on fully invariant subgroups but the group algebra K (F/U) does not satisfy the maximal condition on fully invariant ideals. This solves a problem posed by Plotkin and Vovsi. Using the developed techniques we also construct the first example of a non-finitely based (nilpotent of class 2)-by-(nilpotent of class 2) variety whose Abelian-by-(nilpotent of class at most 2) groups form a hereditarily finitely based subvariety.

Fully Invariant Subgroups of Abelianp-Groups with Finite Ulm–Kaplansky Invariants

2011 ◽  
Vol 39 (11) ◽  
pp. 4273-4282 ◽  
Author(s):  
S. Ya. Grinshpon ◽  
M. M. Nikolskaya (Savinkova)
Keyword(s):  
Fully Invariant Subgroups

The Lattice of Fully Invariant Subgroups of a Cotorsion Hull

2009 ◽  
Vol 16 (1) ◽  
pp. 89-104 ◽  
Author(s):  
Tariel Kemoklidze
Keyword(s):  
Infinite Matrices ◽  
Direct Sum ◽  
Fully Invariant Subgroups

Abstract The paper considers the lattice of fully invariant subgroups of the cotorsion hull of a countable direct sum of torsion-complete p-groups. It is shown that this lattice is isomorphic to the lattice of dual ideals of a semilattice made up of infinite matrices.

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