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arXiv · 1808.07820

An application of blocks to torsion units in group rings

Andreas Bächle·Leo Margolis
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Abstract

We use the theory of blocks of cyclic defect to prove that under a certain condition on the principal p-block of a finite group G the normalized unit group of the integral group ring of G contains an element of order pq if and only if so does G, for q a prime different from p. Using this we verify the Prime Graph Question for all alternating and symmetric groups and also for two sporadic simple groups.

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Andreas Bächle, Leo Margolis. 2018-08-23. An application of blocks to torsion units in group rings. https://doi.org/10.1090/proc/14561

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