Sub-group Test

2-Step Test subgroups:
H subset of group G is subgroup if:
1. H is non-empty
(check: identity of G ∈ H)
2. $Latex a.b^{-1} \in H$

Prove Subset not a subgroup:

1. For infinite Group: sufficient to prove subset doesn't contain e (identity).

2. For finite group: sufficient to prove subset not closed.
H is subgroup of G
$latex \iff a*b^{-1} \in H, \forall a, b \in H$