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On the Prime Graph Question for Integral Group Rings of 4-Primary Groups II

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Abstract

In this article the study of the Prime Graph Question for the integral group ring of almost simple groups which have an order divisible by exactly 4 different primes is continued. We provide more details on the recently developed “lattice method” which involves the calculation of Littlewood-Richardson coefficients. We apply the method obtaining results complementary to those previously obtained using the HeLP-method. In particular the “lattice method” is applied to infinite series of groups for the first time. We also prove the Zassenhaus Conjecture for four more simple groups. Furthermore we show that the Prime Graph Question has a positive answer around the vertex 3 provided the Sylow 3-subgroup is of order 3.

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Acknowledgements

We are very thankful to Markus Schmidmeier for providing us with the link between Littlewood-Richardson coefficients and the structure of finite \(\mathfrak {o}\)-modules.

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Authors and Affiliations

  1. Vakgroep Wiskunde, Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium

    Andreas Bächle

  2. Departamento de Matemáticas, Facultad de Matemáticas, Universidad de Murcia, 30100, Murcia, Spain

    Leo Margolis

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  1. Andreas Bächle
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  2. Leo Margolis
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Correspondence to Leo Margolis.

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Presented by: Steffen Koenig

The first author is supported by the Research Foundation Flanders (FWO - Vlaanderen). The second by the Marie-Curie Individual Fellowship ZC-DLV-705112 from the H2020 program of the European Commission.

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Bächle, A., Margolis, L. On the Prime Graph Question for Integral Group Rings of 4-Primary Groups II. Algebr Represent Theor 22, 437–457 (2019). https://doi.org/10.1007/s10468-018-9776-6

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