Cutting subgroup
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Definition
Definition with symbols
A subgroup of is said to be a cutting subgroup if it is a self-normalizing subgroup and satisfies the further conditions (equivalent subject to the subgroup being self-normalizing):
- There exists a real representation of such that the dimension of is one more than the dimension of ( and are the subspaces comprising points fixed pointwise under the action of and respectively)
- There exists a real representation of such that has dimension 0 and has dimension 1
- There exists an irreducible nontrivial real representation of such that has dimension 1
References
- Equivariant deformations of matrices and real representations by Davide L. Ferrario, Pacific Journal of Mathematics, Vol. 196, No. 2, 2000