Changing the field characteristic on finitary linear groups

1998 ◽  
Vol 70 (2) ◽  
pp. 97-103 ◽  
Author(s):  
Maria Silvia Lucido
Keyword(s):  
Linear Groups ◽  
Field Characteristic ◽  
Finitary Linear

Locally Solvable Finitary Linear Groups

1993 ◽  
Vol s2-47 (1) ◽  
pp. 31-40 ◽  
Author(s):  
Ulrich Meierfrankenfeld ◽  
Richard E. Phillips ◽  
Orazio Puglisi
Keyword(s):  
Linear Groups ◽  
Finitary Linear

Unipotent Finitary Linear Groups

1993 ◽  
Vol s2-48 (1) ◽  
pp. 59-76 ◽  
Author(s):  
Felix Leinen ◽  
Orazio Puglisi
Keyword(s):  
Linear Groups ◽  
Finitary Linear

scholarly journals Irreducible locally nilpotent finitary skew linear groups

1995 ◽  
Vol 38 (1) ◽  
pp. 63-76 ◽  
Author(s):  
B. A. F. Wehrfritz
Keyword(s):  
Linear Group ◽  
Division Ring ◽  
Linear Groups ◽  
Locally Finite ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Finitary Linear Group ◽  
Locally Nilpotent ◽  
Finitary Linear ◽  
Finite Dimensional Case

Let V be a left vector space over the arbitrary division ring D and G a locally nilpotent group of finitary automorphisms of V (automorphisms g of V such that dimDV(g-1)<∞) such that V is irreducible as D-G bimodule. If V is infinite dimensional we show that such groups are very rare, much rarer than in the finite-dimensional case. For example we show that if dimDV is infinite then dimDV = |G| = ℵ0 and G is a locally finite q-group for some prime q ≠ char D. Moreover G is isomorphic to a finitary linear group over a field. Examples show that infinite-dimensional such groups G do exist. Note also that there exist examples of finite-dimensional such groups G that are not isomorphic to any finitary linear group over a field. Generally the finite-dimensional examples are more varied.

scholarly journals Residual Properties of Finitary Linear Groups

1994 ◽  
Vol 166 (2) ◽  
pp. 379-392 ◽  
Author(s):  
B. Bruno ◽  
R.E. Phillips
Keyword(s):  
Linear Groups ◽  
Residual Properties ◽  
Finitary Linear

scholarly journals Maximal Unipotent Subgroups of Finitary Linear Groups

1996 ◽  
Vol 181 (2) ◽  
pp. 628-658 ◽  
Author(s):  
Orazio Puglisi
Keyword(s):  
Linear Groups ◽  
Finitary Linear

On finitary linear groups with a locally nilpotent maximal subgroup

2001 ◽  
Vol 76 (6) ◽  
pp. 401-405
Author(s):  
B. Bruno ◽  
M. Dalle Molle ◽  
F. Napolitani
Keyword(s):  
Maximal Subgroup ◽  
Linear Groups ◽  
Locally Nilpotent ◽  
Finitary Linear ◽  
Nilpotent Maximal Subgroup
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