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Double coset

For subgroups

H, P \leq G

, the double coset of

x \in G

is

H x P = {h x p : h \in H, p \in P} .

The double cosets partition

G

. The action of

H

on the left cosets of

P

gives

\frac{∣ H x P ∣}{∣ P ∣} = \frac{∣ H ∣}{∣ H \cap x P x ^{- 1} ∣}

by the orbit-stabilizer theorem.

Table of contents 87 1
- Sylow subgroup of a subgroup from double cosets Double coset 48

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Solution