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arXiv · 1601.05689

On the Prime Graph Question for Integral Group Rings of 4-primary groups I

Andreas Bächle·Leo Margolis
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Abstract

We study the Prime Graph Question for integral group rings. This question can be reduced to almost simple groups by a result of Kimmerle and Konovalov. We prove that the Prime Graph Question has an affirmative answer for all almost simple groups having a socle isomorphic to $\operatorname{PSL}(2, p^f)$ for $f \leq 2$, establishing the Prime Graph Question for the first time for all automorphic extensions of series of simple groups. Using this, we determine exactly how far the so-called HeLP-method can take us for (almost simple) groups having an order divisible by at most $4$ different primes.

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BibTeXRIS

Andreas Bächle, Leo Margolis. 2016-01-21. On the Prime Graph Question for Integral Group Rings of 4-primary groups I. https://doi.org/10.1142/s0218196717500357

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