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On GL2 of a Local Ring in Which 2 is Not a Unit

Published online by Cambridge University Press:  20 November 2018

A. W. Mason
A. W. Mason*
Affiliation:
Department of Mathematics the University Glasgow, G12 8QW
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Abstract

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Let A be a local ring with maximal ideal m, let N(m ) be the order of the residue field A/m and let N be a subgroup of GLn (A) which is normalized by SLn(A). It follows from results of Klingenberg that N is normal in GLn(A) when n ≥ 3 or . Results of Lacroix show that this is also true when n = 2 and N(m) = 3, provided that N∩2(A) ≠ SL2(A)'.

The principal aim of this paper is to provide examples of non-normal subgroups of GL2(A) which are normalized by SL2(A). In the process we extend results of Lacroix and Levesque on GL2(A)-normalized subgroups of GL2(A), where 2 ∊ m and N(m) > 2.

Keywords

20 H 05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 30 , Issue 2 , 01 June 1987 , pp. 165 - 176
Copyright
Copyright © Canadian Mathematical Society 1987

References

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