English

2-blocks with an abelian defect group and a freely acting cyclic inertial quotient

Representation Theory 2020-10-20 v2 Group Theory

Abstract

We study blocks with an abelian defect group and a cyclic inertial quotient acting freely but not transitively. We prove that when p=2, such blocks are inertial, i.e. basic Morita equivalent to their Brauer correspondent. Together with a result of the second author on Singer cycle actions on homocyclic defect groups, this completes the classification of 2-blocks with a cyclic inertial quotient acting freely on an abelian defect group.

Keywords

Cite

@article{arxiv.2010.08329,
  title  = {2-blocks with an abelian defect group and a freely acting cyclic inertial quotient},
  author = {Cesare Giulio Ardito and Elliot McKernon},
  journal= {arXiv preprint arXiv:2010.08329},
  year   = {2020}
}

Comments

12 pages; improved abstract and statement of main result in v2