Abstract Algebra/Group Theory/Subgroup/Subgroup Inherits Identity
Let H be subgroup of Group G. Let be the binary operation of both H and G
- H and G shares identity
0. Let eH, eG be identities of H and G respectively.
eH is identity of H (usage 1, 3)
eH is identity of H (usage 1)
H is subgroup of G
2. and 3.
4. and eG is identity of G (usage 3)
1. and 5.
cancellation on group G
- If H is subgroup of group G, identity of G is identity of H.
- If H is subgroup of group G, identity of G is in H.