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A Counterexample to the Isomorphism Problem for Integral Group Rings

Martin Hertweck
Annals of Mathematics
Second Series, Vol. 154, No. 1 (Jul., 2001), pp. 115-138
Published by: Annals of Mathematics
DOI: 10.2307/3062112
Stable URL: http://www.jstor.org/stable/3062112
Page Count: 24
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A Counterexample to the Isomorphism Problem for Integral Group Rings
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Abstract

Let X be a finite group, and denote its integral group ring by ZX. A group basis of ZX is a subgroup Y of the group of units of ZX of augmentation 1 such that ZX = ZY and |X| = |y|. An example of a finite group X is given such that ZX has a group basis which is not isomorphic to X. A main ingredient is the existence of a subgroup G of X which possesses a non-inner automorphism which becomes inner in the integral group ring ZG.

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