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arXiv · 1601.00295

Uncountable locally free groups and their group rings

Tsunekazu Nishinaka
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Abstract

In this note, we show that an uncountable locally free group, and therefore every locally free group, has a free subgroup whose cardinality is the same as that of $G$. This result directly improve the main result in [T. Nishinaka,"Group rings of countable non-abelian locally free groups are primitive", Int. J. algebra and computation, 21(3)(2011), 409-431] and establish the primitivity of group rings of locally free groups.

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Tsunekazu Nishinaka. 2016-01-03. Uncountable locally free groups and their group rings. https://arxiv.org/abs/1601.00295

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