Lecture#128Let H be a sub-group of a group G, aH=bH, for a, b belongs to G Iff( a^-1)(b) belong to H

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Let H be a subgroup of a group G and let a, b∈G.Then i) a∈ bH iff aH =bH ii)a∈Hb iff Ha=Hb Let H be a subgroup of a group G and let a, b∈G.Then i) a∈ bH iff aH =bH ii)a∈Hb iff Ha=Hb
H is a subgroup of G iff ab belongs to H for all a,b belongs to H #algebra #maths #groups H is a subgroup of G iff ab belongs to H for all a,b belongs to H #algebra #maths #groups
Theorem -A subset H of group G is subgroup iff a, b belong to H ab^-1 also belong to H Theorem -A subset H of group G is subgroup iff a, b belong to H ab^-1 also belong to H
Group Theory | If a,bϵG and H any sub-group of G then Ha=Hb ⇔ ab^(-1) ϵH and aH=bH ⇔ b^(-1) aϵH | Group Theory | If a,bϵG and H any sub-group of G then Ha=Hb ⇔ ab^(-1) ϵH and aH=bH ⇔ b^(-1) aϵH |
A non-empty subset H of (G, +) is subgroup iff for all a, b in H, a+(-b) belongs to H. A non-empty subset H of (G, +) is subgroup iff for all a, b in H, a+(-b) belongs to H.
(Theorem:19)(part-1) If H is a subgroup of a group G and a,b€G then Ha=Hb iff ab^-1€H (Theorem:19)(part-1) If H is a subgroup of a group G and a,b€G then Ha=Hb iff ab^-1€H
Theorem -A finite subset H of group G is subgroup iff a, b belong to H ab also belong to H Theorem -A finite subset H of group G is subgroup iff a, b belong to H ab also belong to H
A Sub-group H of a Group G is a Normal Sub-group of G, If (aH)(bH)=(abH), for each a, b belongs to G A Sub-group H of a Group G is a Normal Sub-group of G, If (aH)(bH)=(abH), for each a, b belongs to G