Lemma For any subset s of group(g, @ <S> is a subgroup of G Proof: Recall <s>=(s.. Skk) where i1,..., kk are integers So <S> is closed under ·1 is the identity Ik associativity, commutativity still holdLemma For any subset S of group (G,@), <S> is a subgroup of G Proof: Recall <S> = {s1 i1… sk ik } where i1 , …, ik are integers So: • <S> is closed under @ • 1 is the identity • (s1 i1… sk ik ) -1 = s1 -i1… sk -ik • associativity, commutativity still hold