How to Construct Almost Free Groups
- 1 October 1980
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 32 (5) , 1206-1228
- https://doi.org/10.4153/cjm-1980-090-1
Abstract
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.Keywords
This publication has 2 references indexed in Scilit:
- Infinitary stationary logic and abelian groupsFundamenta Mathematicae, 1981
- Methods of logic in abelian group theoryPublished by Springer Nature ,1977