1. Subgroups of odd depth—a necessary condition
- Creator:
- Burciu, Sebastian
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- depth of group algebras, finite group, and faithful representation
- Language:
- English
- Description:
- This paper gives necessary and sufficient conditions for subgroups with trivial core to be of odd depth. We show that a subgroup with trivial core is an odd depth subgroup if and only if certain induced modules from it are faithful. Algebraically this gives a combinatorial condition that has to be satisfied by the subgroups with trivial core in order to be subgroups of a given odd depth. The condition can be expressed as a certain matrix with $\{0,1\}$-entries to have maximal rank. The entries of the matrix correspond to the sizes of the intersections of the subgroup with any of its conjugate.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public