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Proceedings of the American Mathematical Society

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

 

 

The modular group-ring of a finite $ p$-group


Author: D. L. Johnson
Journal: Proc. Amer. Math. Soc. 68 (1978), 19-22
MSC: Primary 20C05
DOI: https://doi.org/10.1090/S0002-9939-1978-0457539-0
MathSciNet review: 0457539
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Abstract: For a finite p-group G and the field k of p elements, we investigate the embedding of G in the group $ {G^\ast}$ of elements of the group-ring kG having coefficient-sum equal to 1. Of particular interest is the question of when G has a normal complement in $ {G^\ast}$, for in this case simple proofs can be given for a number of diverse known results.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0457539-0
Article copyright: © Copyright 1978 American Mathematical Society