Definition:
Subgroup :
A non empty subset H of a group G is called a subgroup of G , if H itself is a groupw.r.t.the same binary operation as in G.
Def. Proper and Improper subgroups :
For a group G, the set {e} and G are always subgroups of G and are called improper subgroups of G.
Any other subgroup [other than G and {e}] is called a proper subgroup
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