Difference between revisions of "Subgroup"

Revision as of 17:23, 15 March 2015

A subgroup $(H,\times_H:H\times H\rightarrow H$ of a Group $(G,\times_G:G\times G\rightarrow G)$ is a set $H\subseteq G$ which is a group under the operation $\times_G$ restricted to $H\times H$.

Definition

Given a group $(G,\times_G:G\times G\rightarrow G)$ we say $(H,\times_H:H\times H\rightarrow H)$ is a subgroup of $(G,\times_G)$ if: