Cutting subgroup

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History

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Definition

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

References

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

External links

• Online link for Ferrario's paper