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How to Construct Almost Free Groups

Published online by Cambridge University Press:  20 November 2018

Alan H. Mekler
Alan H. Mekler*
Affiliation:
University of Toronto, Toronto, Ontario
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Almost free groups were introduced in [9] as groups all of whose “small” subgroups are free. Here “small” means generated by fewer elements than the cardinality of the group. This concept is a generalization of locally free. Suppose κ is a cardinal > ω. A group is κ-free if every subgroup generated by fewer than κ elements is free. A group of cardinality κ which is κ-free is almost free. There are two related concepts which are closer approximations to freeness.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 5 , 01 October 1980 , pp. 1206 - 1228
Copyright
Copyright © Canadian Mathematical Society 1980

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