Cutting subgroup

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Definition with symbols

A subgroup H of G 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 V of G such that the dimension of V^H is one more than the dimension of V^G (V^H and V^G are the subspaces comprising points fixed pointwise under the action of H and G respectively)
  • There exists a real representation V of G such that V^G has dimension 0 and V^H has dimension 1
  • There exists an irreducible nontrivial real representation V of G such that V^H has dimension 1


  • Equivariant deformations of matrices and real representations by Davide L. Ferrario, Pacific Journal of Mathematics, Vol. 196, No. 2, 2000

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