scholarly journals On non-Abelian infinite-dimensional linear groups

2021 ◽  
Vol 16 ◽  
pp. 56
Author(s):  
O.Yu. Dashkova
Keyword(s):  
Abelian Subgroup ◽  
Linear Groups ◽  
Infinite Dimensional

We study non-Abelian solvable infinite-dimensional linear groups of infinite $p$-rank ($р \geqslant 0$) and of infinite fundamental dimensionality, whose any proper non-Abelian subgroup of infinite $p$-rank has finite fundamental dimensionality. We obtain the description of structure of groups from this class.

ON SOME INFINITE DIMENSIONAL LINEAR GROUPS

2001 ◽  
Vol 29 (2) ◽  
pp. 519-527
Author(s):  
L. A. Kurdachenko ◽  
I. Ya. Subbotin
Keyword(s):  
Linear Groups ◽  
Infinite Dimensional

scholarly journals Generalisations of nilpotency of rings

1973 ◽  
Vol 18 (4) ◽  
pp. 265-272 ◽  
Author(s):  
Edmund F. Robertson
Keyword(s):  
Linear Groups ◽  
Infinite Dimensional

In (5) and (6) we studied certain subgroups of infinite dimensional linear groups over rings. In particular we investigated how the structure of the subgroups was related to the structure of the rings over which the linear groups were defined. It became clear that it might prove useful to study generalised nilpotent properties of rings analogous to Baer nilgroups and Gruenberg groups. We look briefly at some classes of generalised nilpotent rings in this paper and obtain a lattice diagram exhibiting all the strict inclusions between the classes.

On an analogue of a theorem of P. Hall for infinite dimensional linear groups

2019 ◽  
Vol 6 (2) ◽  
pp. 577-589
Author(s):  
Martyn R. Dixon ◽  
Leonid A. Kurdachenko ◽  
Igor Ya. Subbotin
Keyword(s):  
Linear Groups ◽  
Infinite Dimensional

Infinite dimensional linear groups

1978 ◽  
Vol 78 (3-4) ◽  
pp. 237-240 ◽  
Author(s):  
D. G. Arrell ◽  
E. F. Robertson
Keyword(s):  
Linear Group ◽  
General Linear Group ◽  
Normal Structure ◽  
General Linear ◽  
Noetherian Rings ◽  
Linear Groups ◽  
Infinite Dimensional

SynopsisIn this paper we show that some of Bass' results on the normal structure of the stable general linear group can be extended to infinite dimensional linear groups over non-commutative Noetherian rings.

scholarly journals On the structure of some infinite dimensional linear groups

2016 ◽  
Vol 45 (1) ◽  
pp. 234-246 ◽  
Author(s):  
Martyn R. Dixon ◽  
Leonid A. Kurdachenko ◽  
Javier Otal
Keyword(s):  
Linear Groups ◽  
Infinite Dimensional

On some infinite dimensional linear groups

2009 ◽  
Vol 7 (2) ◽  
Author(s):  
Leonid Kurdachenko ◽  
Alexey Sadovnichenko ◽  
Igor Subbotin
Keyword(s):  
Vector Space ◽  
Present Article ◽  
Linear Groups ◽  
Infinite Dimensional

AbstractLet 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.

On some infinite dimensional linear groups

2003 ◽  
pp. 377-384 ◽  
Author(s):  
Leonid Kurdachenko ◽  
Igor Subbotin
Keyword(s):  
Linear Groups ◽  
Infinite Dimensional
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