Let H be a subgroup of group G. Then the identity element of H is same as the identity element of G.

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Sub-groups/identity of H and G same ,inverse of H and G same/unit-2/3rd sem/In Telugu Sub-groups/identity of H and G same ,inverse of H and G same/unit-2/3rd sem/In Telugu
Let H be a subgroup of G, and let a belong to G. Then a belongs to aH Let H be a subgroup of G, and let a belong to G. Then a belongs to aH
Group Theory | Subgroup | Subgroup Theorems | Discrete Mathematics Group Theory | Subgroup | Subgroup Theorems | Discrete Mathematics
Let H be subgroup of a group G and let a, b∈G.Then i) aH =bH iff a^-1b∈ H ii)Ha=Hb iff ab^-1∈H Let H be subgroup of a group G and let a, b∈G.Then i) aH =bH iff a^-1b∈ H ii)Ha=Hb iff ab^-1∈H
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let g be an element (non-identity) of a group G then g is its own inverse iff g is of order 2 let g be an element (non-identity) of a group G then g is its own inverse iff g is of order 2
9.In a group G | The identity element is unique | Inverse of each element is unique 9.In a group G | The identity element is unique | Inverse of each element is unique