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Proceedings of the American Mathematical Society

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

 
 

 

Units in modular group rings


Authors: D. B. Coleman and D. S. Passman
Journal: Proc. Amer. Math. Soc. 25 (1970), 510-512
MSC: Primary 20.40
DOI: https://doi.org/10.1090/S0002-9939-1970-0262360-5
MathSciNet review: 0262360
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Abstract: Let $G$ be a finite $p$-group and let $U(G)$ denote the group of normalized units in the modular group ring of $G$. If $G$ is nonabelian, then it is shown that the nonregular group ${Z_p}\wr {Z_p}$ is involved in $U(G)$. Here ${Z_p}$ is the group with $p$ elements and ${Z_p}\wr {Z_p}$ is wreath product.


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Keywords: <IMG WIDTH="16" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="$p$">-group, group ring, group of units
Article copyright: © Copyright 1970 American Mathematical Society