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Constructing free subgroups of integral group ring units

Author(s): Zbigniew S. Marciniak; Sudarshan K. Sehgal
Journal: Proc. Amer. Math. Soc. 125 (1997), 1005-1009.
MSC (1991): Primary 16S34, 16U60
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Abstract: Let $G$ be an arbitrary group. It is proved that if $\mathbb {Z}G$ contains a bicyclic unit $u\ne 1$ , then $\langle u,u^*\rangle$ is a nonabelian free subgroup of invertible elements.

References:

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2.: E. Jespers, Free normal complements and the unit group of integral group rings, Proceedings of AMS 122 (1994), 59-66. MR 94k:16058
3.: E. Jespers, G. Leal, and A. del Rio, Products of free groups in the unit group of integral group rings, J. Algebra 180 (1996), 22-40. CMP 96:08
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5.: D. S. Passman, Algebraic structure of group rings, Interscience, New York, 1977. MR 81d:16001
6.: S. K. Sehgal, Units in integral group rings, Longman's, Essex, 1993. MR 94m:16039
7.: S. K. Sehgal, Topics in group rings, Marcel Dekker, 1978. MR 80j:16001


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