ON CONJUGACY CLASSES IN LINEAR GROUPS

1993 ◽  
Vol 26 (2) ◽  
Author(s):  
Jan Ambrosiewicz
Keyword(s):  
Conjugacy Classes ◽  
Linear Groups

Conjugacy classes of small sizes in the linear and unitary groups

2013 ◽  
Vol 16 (6) ◽  
Author(s):  
Shawn T. Burkett ◽  
Hung Ngoc Nguyen
Keyword(s):  
Conjugacy Classes ◽  
Unitary Groups ◽  
General Linear ◽  
Linear Groups ◽  
Classical Groups ◽  
General Linear Groups ◽  
Finite Classical Groups

Abstract.Using the classical results of G. E. Wall on the parametrization and sizes of (conjugacy) classes of finite classical groups, we present some gap results for the class sizes of the general linear groups and general unitary groups as well as their variations. In particular, we identify the classes in

scholarly journals Conjugacy classes in linear groups

1977 ◽  
Vol 44 (2) ◽  
pp. 339-362 ◽  
Author(s):  
N Burgoyne ◽  
R Cushman
Keyword(s):  
Conjugacy Classes ◽  
Linear Groups

scholarly journals Conjugacy classes in projective and special linear groups

1980 ◽  
Vol 22 (3) ◽  
pp. 339-364 ◽  
Author(s):  
G.E. Wall
Keyword(s):  
Finite Field ◽  
Conjugacy Classes ◽  
Linear Groups ◽  
Commutative Field ◽  
Special Linear ◽  
Projective Special Linear Groups ◽  
Special Linear Groups ◽  
Finite Dimensional

The conjugacy classes in the finite-dimensional projective full linear, special linear and projective special linear groups over an arbitrary commutative field are determined. The results over a finite field are applied to certain enumerative problems.

scholarly journals Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups

2014 ◽  
Vol 57 (1) ◽  
pp. 132-140 ◽  
Author(s):  
T. Mubeena ◽  
P. Sankaran
Keyword(s):  
Hyperbolic Group ◽  
Complete Riemannian Manifold ◽  
Abelian Extension ◽  
Conjugacy Classes ◽  
Linear Groups ◽  
Congruence Subgroups ◽  
Group Automorphism ◽  
Abelian Extensions ◽  
Twisted Conjugacy ◽  
Torsion Free

AbstractGiven a group automorphismϕ: Γ → Γ, one has an action of Γ on itself byϕ-twisted conjugacy, namely,g.x = gxϕ(g-1). The orbits of this action are calledϕ-twisted conjugacy classes. One says that Γ has theR∞-property if there are infinitely manyϕ-twisted conjugacy classes for every automorphismϕof Γ. In this paper we show that SL(n; Z) and its congruence subgroups have the R8-property. Further we show that any (countable) abelian extension of Γ has the R8-property where Γ is a torsion free non-elementary hyperbolic group, or SL(n; Z); Sp(2n; Z) or a principal congruence subgroup of SL(n; Z) or the fundamental group of a complete Riemannian manifold of constant negative curvature.

scholarly journals Linear Groups with Restricted Conjugacy Classes

2021 ◽  
Author(s):  
F. de Giovanni ◽  
M. Trombetti ◽  
B. A. F. Wehrfritz
Keyword(s):  
Conjugacy Classes ◽  
Linear Groups

AbstractIn this paper we characterize, in terms of their conjugacy classes, linear groups G such that $$G/\zeta _k(G)$$ G / ζ k ( G ) belongs to a certain group class $$\mathfrak {X}$$ X for several natural choices of $$\mathfrak {X}$$ X . Moreover, a description is given of linear groups with restrictions on layers.

Conjugacy classes of maximal soluble subgroups of the general linear groups

2010 ◽  
pp. 127-131
Author(s):  
Simon R. Blackburn ◽  
Peter M. Neumann ◽  
Geetha Venkataraman
Keyword(s):  
Conjugacy Classes ◽  
General Linear ◽  
Linear Groups ◽  
General Linear Groups
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