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Trivial source character tables of Frobenius groups of type (Cp×Cp)⋊H

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Original languageEnglish
Number of pages28
Publication statusE-pub ahead of print - 21 Mar 2024

Abstract

Let p be a prime number. We compute the trivial source character tables Triv_p(G) of finite Frobenius groups G with an abelian Frobenius complement H and an elementary abelian Frobenius kernel of order p2. More precisely, we deal with all infinite families of such groups which occur in the two extremal cases for the fusion of p-subgroups: the case in which there exists exactly one G-conjugacy class of non-trivial cyclic p-subgroups, and the case in which there exist exactly p+1 distinct G-conjugacy classes of non-trivial cyclic p-subgroups.

Keywords

    Frobenius groups, trivial source modules, projective indecomposable modules, p-permutation modules, trivial source character tables, ordinary character theory, decomposition matrices, simple modules

Cite this

Lassueur C, Böhmler BK. Trivial source character tables of Frobenius groups of type (Cp×Cp)⋊H. 2024 Mar 21. Epub 2024 Mar 21. doi: 10.48550/arXiv.2403.14571
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abstract = "Let p be a prime number. We compute the trivial source character tables Triv_p(G) of finite Frobenius groups G with an abelian Frobenius complement H and an elementary abelian Frobenius kernel of order p2. More precisely, we deal with all infinite families of such groups which occur in the two extremal cases for the fusion of p-subgroups: the case in which there exists exactly one G-conjugacy class of non-trivial cyclic p-subgroups, and the case in which there exist exactly p+1 distinct G-conjugacy classes of non-trivial cyclic p-subgroups.",
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AU - Böhmler, Bernhard Karl

PY - 2024/3/21

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N2 - Let p be a prime number. We compute the trivial source character tables Triv_p(G) of finite Frobenius groups G with an abelian Frobenius complement H and an elementary abelian Frobenius kernel of order p2. More precisely, we deal with all infinite families of such groups which occur in the two extremal cases for the fusion of p-subgroups: the case in which there exists exactly one G-conjugacy class of non-trivial cyclic p-subgroups, and the case in which there exist exactly p+1 distinct G-conjugacy classes of non-trivial cyclic p-subgroups.

AB - Let p be a prime number. We compute the trivial source character tables Triv_p(G) of finite Frobenius groups G with an abelian Frobenius complement H and an elementary abelian Frobenius kernel of order p2. More precisely, we deal with all infinite families of such groups which occur in the two extremal cases for the fusion of p-subgroups: the case in which there exists exactly one G-conjugacy class of non-trivial cyclic p-subgroups, and the case in which there exist exactly p+1 distinct G-conjugacy classes of non-trivial cyclic p-subgroups.

KW - Frobenius groups

KW - trivial source modules

KW - projective indecomposable modules

KW - p-permutation modules

KW - trivial source character tables

KW - ordinary character theory

KW - decomposition matrices

KW - simple modules

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DO - 10.48550/arXiv.2403.14571

M3 - Preprint

BT - Trivial source character tables of Frobenius groups of type (Cp×Cp)⋊H

ER -

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