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Caroline Lassueur

Publications and source records attributed to Caroline Lassueur.

At least 19 recordsLinked to original sources
arXiv2026

On the source algebra equivalence class of blocks with cyclic defect groups, III

This series of papers is a contribution to the program of classifying $p$-blocks of finite groups up to source algebra equivalence, starting with the case of cyclic blocks. To any $p$-block $\mathbf{B}$ of a finite group with cyclic defect group $D$, Linckelmann associated an invariant $W( \mathbf{B} )$, which is an indecomposable endo-permutation module over $D$, and which, together with the Brauer tree of~$\mathbf{B} $, essentially determines its source algebra equivalence class. In Part II of our series, assuming that $p$ is an odd prime, we reduced the classification of the invariants $W( \mathbf{B} )$ arising from cyclic $p$-blocks $\mathbf{B}$ of quasisimple classical groups to the classification for cyclic $p$-blocks of quasisimple quotients of special linear or unitary groups. This objective is achieved in the present Part III.

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arXiv2025

On the source algebra equivalence class of blocks with cyclic defect groups, II

This series of papers is a contribution to the program of classifying $p$-blocks of finite groups up to source algebra equivalence, starting with the case of cyclic blocks. To any $p$-block $\mathbf{B}$ of a finite group with cyclic defect group $D$, Linckelmann associated an invariant $W( \mathbf{B} )$, which is an indecomposable endo-permutation module over $D$, and which, together with the Brauer tree of $\mathbf{B}$, essentially determines its source algebra equivalence class. In Parts II-IV of our series of papers, we classify, for odd $p$, those endo-permutation modules of cyclic $p$-groups arising from $p$-blocks of quasisimple groups. In the present Part II, we reduce the desired classification for the quasisimple classical groups of Lie type $B$, $C$, and $D$ to the corresponding objective for the general linear and unitary groups; the classification is completed for the latter groups.

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arXiv2024

Principal 2-blocks with wreathed defect groups up to splendid Morita equivalence

We classify principal $2$-blocks of finite groups $G$ with Sylow $2$-subgroups isomorphic to a wreathed $2$-group $C_{2^n}\wr C_2$ with $n\geq 2$ up to Morita equivalence and up to splendid Morita equivalence. As a consequence, we obtain that Puig's Finiteness Conjecture holds for such blocks. Furthermore, we obtain a classification of such groups modulo $O_{2'}(G)$, which is a pure group theoretical result and of independent interest. Methods previously applied to blocks of tame representation type are used. They are, however, further developed in order to deal with blocks of wild representation type.

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arXiv2024

Trivial source character tables of Frobenius groups of type $(C_p \times C_p) \rtimes H$

Let $p$ be a prime number. We compute the trivial source character tables of finite Frobenius groups $G$ with an abelian Frobenius complement $H$ and an elementary abelian Frobenius kernel of order $p^2$. 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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arXiv2022

On the source algebra equivalence class of blocks with cyclic defect groups, I

We investigate the source algebra class of a p-block with cyclic defect groups of the group algebra of a finite group. By the work of Linckelmann this class is parametrized by the Brauer tree of the block together with a sign function on its vertices and an endo-permutation module of a defect group. We prove that this endo-permutation module can be read off from the character table of the group. We also prove that this module is trivial for all cyclic p-blocks of quasisimple groups with a simple quotient which is a sporadic group, an alternating group, a group of Lie type in defining characteristic, or a group of Lie type in cross-characteristic for which the prime p is large enough in a certain sense.

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arXiv2022

Trivial source character tables of $\text{SL}_2(q)$, Part II

We compute the trivial source character tables (also called species tables of the trivial source ring) of the infinite family of finite groups $\text{SL}_{2}(q)$ for $q$ even, over a large enough field $k$ of positive characteristic ${\ell}$ not dividing $q$. This article is a continuation of our article Trivial Source Character Tables of $\text{SL}_{2}(q)$ where we considered, in particular, the case in which $q$ is odd in cross-characteristic.

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arXiv2021

Trivial source character tables of SL(2,q)

We compute the trivial source character tables (also called species tables of the trivial source ring) of the infinite family of finite groups SL(2,q) over a large enough field of positive characteristic $\ell$ via character-theoretical methods in the cases in which $q$ is odd, $\ell \mid (q\pm1)$ when~$\ell$ is odd, and $q\equiv \pm 3\pmod{8}$ when $\ell=2$.

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arXiv2020

The classification of the trivial source modules in blocks with cyclic defect groups

Relying on the classification of the indecomposable liftable modules in arbitrary blocks with non-trivial cyclic defect groups we give a complete classification of the trivial source modules lying in such blocks, describing in particular their associated path on the Brauer tree of the block in the sense of Janusz (1969). The appendix contains a description of the minimal distance from an arbitrary non-projective indecomposable liftable module to the boundary of the stable Auslander-Reiten quiver of the block.

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arXiv2020

Trivial source characters in blocks with cyclic defect groups

We describe the ordinary characters of trivial source modules lying in blocks with cyclic defect groups relying on their recent classification in terms of paths on the Brauer tree by G.~Hiss and the second author. In particular, we show how to recover the exceptional constituents of such characters using the source algebra of the block.

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arXiv2019

Splendid Morita equivalences for principal 2-blocks with dihedral defect groups

Given a dihedral $2$-group $P$ of order at least~8, we classify the splendid Morita equivalence classes of principal $2$-blocks with defect groups isomorphic to $P$. To this end we construct explicit stable equivalences of Morita type induced by specific Scott modules using Brauer indecomposability and gluing methods; we then determine when these stable equivalences are actually Morita equivalences, and hence automatically splendid Morita equivalences. Finally, we compute the generalised decomposition numbers in each case.

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arXiv2018

On the lifting of the Dade group

For the group of endo-permutation modules of a finite \(p\)-group, there is a surjective reduction modulo \(p\) homomorphism from a complete discrete valuation ring of characteristic 0 to its residue field of characteristic \(p\). We prove that this reduction map always has a section which is a group homomorphism.

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arXiv2017

Simple modules in the Auslander-Reiten quiver of principal blocks with abelian defect groups

Given an odd prime $p$, we investigate the position of simple modules in the stable Auslander-Reiten quiver of the principal block of a finite group with non-cyclic abelian Sylow $p$-subgroups. In particular, we prove a reduction to finite simple groups. In the case that the characteristic is $3$, we prove that simple modules in the principal block all lie at the end of their components

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arXiv2015

Endo-trivial modules for finite groups with dihedral Sylow 2-subgroup

Let $k$ be an algebraically closed field of characteristic $p>0$ and $G$ a finite group. We provide a description of the torsion subgroup $TT(G)$ of the finitely generated abelian group $T(G)$ of endo-trivial $kG$-modules when $p=2$ and $G$ has a dihedral Sylow $2$-subgroup $P$. We prove that, in the case $|P|\geq 8$, $TT(G)\cong X(G)$ the group of one-dimensional $kG$-modules, except possibly when $G/O_{2'}(G)\cong \mathfrak{A}_6$, the alternating group of degree $6$; in which case $G$ may have $9$-dimensional simple torsion endo-trivial modules. We also prove a similar result in the case $|P|=4$, although the situation is more involved. Our results complement the tame-representation type investigation of endo-trivial modules started by Carlson-Mazza-Thévenaz in the cases of semi-dihedral and generalized quaternion Sylow 2-subgroups. Furthermore we provide a general reduction result, valid at any prime $p$, to recover the structure of $TT(G)$ from the structure of $TT(G/H)$, where $H$ is a normal $p'$-subgroup of $G$.

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