Ivan Shishkin, Birch Grove

Subgroup

Definition / General algebra / Usable

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Usable. This concept is clear enough to use, but has not yet been reviewed by another trusted user.

A subgroup of a group GG is a subset H⊆GH\subseteq G that is itself a group under the same operation.

Practice this concept with exercises

  • Montrer que HH est un sous-groupe de (G, ⋅ )(G, \ \cdot \ ) si et seulement si, pour tous x,y∈Hx,y \in H, xy−1∈Hxy^{-1} \in H.

    Open exercise
Problems using this concept (1)
Quotient of a group and subgroup
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