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Improving tameness for metabelian groups.

Bogley, W.A., Harlander, J. (2004)

The New York Journal of Mathematics [electronic only]

Infinite dimensional linear groups with a large family of $G$ -invariant subspaces

L. A. Kurdachenko, A. V. Sadovnichenko, I. Ya. Subbotin (2010)

Commentationes Mathematicae Universitatis Carolinae

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 $B$ is called almost $G$ -invariant, if ${dim}_{F} (B / {Core}_{G} (B))$ is finite. In the current article, we begin the study of those subgroups $G$ of $GL (F, A)$ for which every subspace of $A$ is almost $G$ -invariant. More precisely, we consider the case when $G$ is a periodic group. We prove that in this case $A$ includes a $G$ -invariant subspace $B$ of finite codimension whose subspaces are $G$ -invariant.

Infinite dimensional linear groups with many G - invariant subspaces

Leonid Kurdachenko, Alexey Sadovnichenko, Igor Subbotin (2010)

Open Mathematics

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.

Infinite Soluble Groups with Engel Cycles; a Finiteness Condition.

Rolf Brandl (1983)

Mathematische Zeitschrift

Infinite soluble groups with no outer automorphisms

Derek J. S. Robinson (1980)

Rendiconti del Seminario Matematico della Università di Padova

Infinite Soluble Groups with the Bell Property: A Finiteness Condition.

Rolf Brandl (1987)

Monatshefte für Mathematik

Infinitely Generated Subgroups of Finitely Presented Groups. Part II.

Gilbert, Cannonito, F.B. Baumslag (1980)

Mathematische Zeitschrift

Injectors of fitting classes of $\mathfrak{G}_{1}$ -groups

Federico Menegazzo, Martin L. Newell (1988)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Fitting classes and injectors are discussed in the class of $\mathfrak{G}_{1}$ -groups. A necessary and sufficient condition for the existence of injectors is given; it is also shown that, when this condition holds, the injectors form a unique conjugacy class.

Isomorphism of noncommutative group algebras of torsion-free groups over a field.

Danchev, P.V. (2005)

Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică

Isoperimetric inequalities and the homology of groups.

G. Baumslag, H. Short, C. III. Miller (1993)

Inventiones mathematicae

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