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Maximal normal subgroups of the integral linear group of countable degree

Published online by Cambridge University Press:  17 April 2009

R.G. Burns  and
I.H. Farouqi
R.G. Burns
Affiliation:
Department of Mathematics, York University, Toronto, Canada;
I.H. Farouqi
Affiliation:
Department of Mathematics, University of New England, Armidale, New South Wales.
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Abstract

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This paper continues the second author's investigation of the normal structure of the automorphism group г of a free abelian group of countably infinite rank. It is shown firstly that, in contrast with the case of finite degree, for each prime p every linear transformation of the vector space of countably infinite dimension over Zp, the field of p elements, is induced by an element of г Since by a result of Alex Rosenberg GL(אo, Zp ) has a (unique) maximal normal subgroup, it then follows that г has maximal normal subgroups, one for each prime.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 15 , Issue 3 , December 1976 , pp. 439 - 451
Copyright
Copyright © Australian Mathematical Society 1976

References

[1]Brenner, J.L., “The linear homogeneous group, III”, Ann. of Math. 71 (1960), 210–223.CrossRefGoogle Scholar
[2]Farouqi, I.H., “On an infinite integral linear group”, Bull. Austral. Math. Soc. 4 (1971), 321–342.CrossRefGoogle Scholar
[3]Mennicke, Jens L., “Finite factor groups of the unimodular group”, Ann. of Math. 81 (1965), 31–37.CrossRefGoogle Scholar
[4]Rosenberg, Alex, “The structure of the infinite general linear group”, Ann. of Math. 68 (1958), 278–294.CrossRefGoogle Scholar