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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the applications of coalgebras to group algebras


Author: Alan Rosenberg
Journal: Proc. Amer. Math. Soc. 52 (1975), 109-112
MSC: Primary 16A26
DOI: https://doi.org/10.1090/S0002-9939-1975-0382331-2
MathSciNet review: 0382331
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Abstract: This paper examines the coalgebra structure on $ k{[G]^ \circ }$ and relates it to the group theoretic properties of $ G$. In particular it is shown that there is an intimate relation between $ k[G]$ being proper and $ G$ being residually finite. We use this to derive a series of conditions on the group to guarantee it being residually finite.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0382331-2
Keywords: Coalgebra, group algebra, proper, residually finite
Article copyright: © Copyright 1975 American Mathematical Society

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