Commit 2022-10-24 07:29 3882aaf6
View on Github →feat(group_theory/index): criterion for subgroups of index two (#16629)
- A subgroup has index two if and only if there exists
a
such that for allb
,b * a ∈ H
is equivalent tob ∉ H
. - For a subgroup of index two,
a * b ∈ H ↔ (a ∈ H ↔ b ∈ H)
.