Normal Subgroups of Orthogonal Groups Over Commutative Rings

1988 ◽  
Vol 110 (5) ◽  
pp. 955 ◽  
Author(s):  
L. N. Vaserstein
Keyword(s):  
Commutative Rings ◽  
Normal Subgroups ◽  
Orthogonal Groups

scholarly journals Existence of finite groups with classical commutator subgroup

1978 ◽  
Vol 25 (1) ◽  
pp. 41-44 ◽  
Author(s):  
Michael D. Miller
Keyword(s):  
Abelian Group ◽  
Finite Fields ◽  
Finite Groups ◽  
Commutator Subgroup ◽  
Unitary Groups ◽  
The Other ◽  
Linear Groups ◽  
Normal Subgroups ◽  
Orthogonal Groups ◽  
General Linear Groups

AbstractGiven a group G, we may ask whether it is the commutator subgroup of some group G. For example, every abelian group G is the commutator subgroup of a semi-direct product of G x G by a cyclic group of order 2. On the other hand, no symmetric group Sn(n>2) is the commutator subgroup of any group G. In this paper we examine the classical linear groups over finite fields K of characteristic not equal to 2, and determine which can be commutator subgroups of other groups. In particular, we settle the question for all normal subgroups of the general linear groups GLn(K), the unitary groups Un(K) (n≠4), and the orthogonal groups On(K) (n≧7).

Sign in / Sign up

Export Citation Format

Share Document