Groups

Subgroups:

Let (G,*) be a group and H be a non-empty subset of G. H is said to be subgroup under * if

Definition.

Let (G, *) be a group and H be a non-empty subset of G. If (H,*) is a group where * is the induced composition, then (H,*) is said to be a subgroup of the group (G,*).

Example:

(Q ,+) is a group. Z is a non-empty subset of Q and (Z,+) is a group. Therefore (Z,+) is a subgroup of the group (Q ,+).