Let us consider that S is subset of group G such that S = { x in G ; x^2=e } Where e is identity element of G. then prove that S is subgroup.
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Let us consider that S is subset of group G such that
S = { x in G ; x^2=e }
Where e is identity element of G. then prove that S is subgroup.
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- 32. Let be a fixed element of the group . According to Exercise 20 of section 3.5, the mapping defined by is an automorphism of . Each of these automorphism is called an inner automorphism of . Prove that the set forms a normal subgroup of the group of all automorphism of . Exercise 20 of Section 3.5 20. For each in the group , define a mapping by . Prove that is an automorphism of .Let be a group of order 24. If is a subgroup of , what are all the possible orders of ?Let H and K be subgroups of a group G and K a subgroup of H. If the order of G is 24 and the order of K is 3, what are all the possible orders of H?