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The free centre-by-metabelian groups

Published online by Cambridge University Press:  09 April 2009

Chander Kanta Gupta
Chander Kanta Gupta
Affiliation:
University of Manitoba Winnipeg, Manitoba Canada
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Let be the free centre-by-metabelian group of rank n. In this paper, our main result is the following

Theorem. For n ≧ 4, Gn has a finite elementary abelian subgroup Hn of rank . More precisely, Hn is a minimal fully invariant subgroup contained in the centre of Gn and Gn/Hn is isomorphic to a group of 3 x 3 matrices over a finitely generated integral domain of characteristic zero.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 16 , Issue 3 , November 1973 , pp. 294 - 299
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Gupta, C. K., ‘A faithful matrix representation for certain centre-by-metabelian groups’, J. Austral. Math. Soc. 10 (1969), 451–464.CrossRefGoogle Scholar
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