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Finite one-relator products of two cyclic groups with the relator of arbitrary length
Published online by Cambridge University Press: 09 April 2009
Abstract
In this paper we consider the groups G = G(α, n) defined by the presentations . We derive a formula for [G′: ″] and determine the order of G whenever n ≦ 7. We show that G is a finite soluble group if n is odd, but that G can be infinite when n is even, n ≧ 8. We also show that G(6, 10) is a finite insoluble group involving PSU(3, 4), and that the group H with presentation is a finite group of deficiency zero of order at least 114,967,210,176,000.
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 53 , Issue 3 , December 1992 , pp. 352 - 368
- Copyright
- Copyright © Australian Mathematical Society 1992
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