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Direct decompositions of groups with finitely generated commutator quotient group

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Ronald Hirshon
Ronald Hirshon
Affiliation:
Mathematics Department Polytechnic Institute of New York333 Jay Street Brooklyn, N.Y. 11201, U.S.A.
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Abstract

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Let G/G' be finitely generated and let G = B1 x A1 = B2 x A2 = … = Bi x Ai = … with each Bi isomorphic to a fixed group B which obeys the maximal condition for normal subgroups. Then the Ai represent only finitely many isomorphism classes. We give an example with B infinite cyclic, G/G' free abelian of infinite (countable) rank and such that G is decomposed as above with no two Ai isomorphic.

MSC classification

Secondary: 20F06: Cancellation theory; application of van Kampen diagrams 20E22: Extensions, wreath products, and other compositions 20E15: Chains and lattices of subgroups, subnormal subgroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 3 , November 1979 , pp. 315 - 320
Copyright
Copyright © Australian Mathematical Society 1979

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