# Endotrivial modules over groups with quaternion or semi-dihedral Sylow 2-subgroup

Jon F. Carlson; Nadia Mazza; Jacques Thévenaz

Journal of the European Mathematical Society (2013)

- Volume: 015, Issue: 1, page 157-177
- ISSN: 1435-9855

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topCarlson, Jon F., Mazza, Nadia, and Thévenaz, Jacques. "Endotrivial modules over groups with quaternion or semi-dihedral Sylow 2-subgroup." Journal of the European Mathematical Society 015.1 (2013): 157-177. <http://eudml.org/doc/277169>.

@article{Carlson2013,

abstract = {Let $G$ be a finite group with a Sylow 2-subgroup $P$ which is either quaternion or semi-dihedral. Let $k$ be an algebraically closed field of characteristic 2. We prove the existence of exotic endotrivial $kG$-modules, whose restrictions to $P$ are isomorphic to the direct sum of the known exotic endotrivial $kP$-modules and some projective modules. This provides a description of the group $T(G)$ of endotrivial $kG$-modules.},

author = {Carlson, Jon F., Mazza, Nadia, Thévenaz, Jacques},

journal = {Journal of the European Mathematical Society},

keywords = {groups of endotrivial modules; exotic endotrivial modules; semi-dihedral groups; generalized quaternion groups; almost split sequences; syzygies; Sylow 2-subgroups; stable isomorphisms; groups of endotrivial modules; exotic endotrivial modules; semi-dihedral groups; generalized quaternion groups; almost split sequences; syzygies; Sylow 2-subgroups; stable isomorphisms},

language = {eng},

number = {1},

pages = {157-177},

publisher = {European Mathematical Society Publishing House},

title = {Endotrivial modules over groups with quaternion or semi-dihedral Sylow 2-subgroup},

url = {http://eudml.org/doc/277169},

volume = {015},

year = {2013},

}

TY - JOUR

AU - Carlson, Jon F.

AU - Mazza, Nadia

AU - Thévenaz, Jacques

TI - Endotrivial modules over groups with quaternion or semi-dihedral Sylow 2-subgroup

JO - Journal of the European Mathematical Society

PY - 2013

PB - European Mathematical Society Publishing House

VL - 015

IS - 1

SP - 157

EP - 177

AB - Let $G$ be a finite group with a Sylow 2-subgroup $P$ which is either quaternion or semi-dihedral. Let $k$ be an algebraically closed field of characteristic 2. We prove the existence of exotic endotrivial $kG$-modules, whose restrictions to $P$ are isomorphic to the direct sum of the known exotic endotrivial $kP$-modules and some projective modules. This provides a description of the group $T(G)$ of endotrivial $kG$-modules.

LA - eng

KW - groups of endotrivial modules; exotic endotrivial modules; semi-dihedral groups; generalized quaternion groups; almost split sequences; syzygies; Sylow 2-subgroups; stable isomorphisms; groups of endotrivial modules; exotic endotrivial modules; semi-dihedral groups; generalized quaternion groups; almost split sequences; syzygies; Sylow 2-subgroups; stable isomorphisms

UR - http://eudml.org/doc/277169

ER -

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