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If $G$ is a group, a subset $H\subseteq G$ is a subgroup of $G$ if the binary operation of $G$ restricts to a binary operation on $H$, and $H$ is a group for this induced operation.

Equivalently, the subset $H$ must satisfy the following conditions:

  1. for all $a,b\in H$, $a*b\in H$
  2. the identity of $G$ is an element of $H$
  3. for every $a\in H$, the inverse of $a$ in $G$ is also in $H$.
Knowl status:
  • Review status: reviewed
  • Last edited by John Jones on 2018-08-06 04:03:10
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