What are the possible orders of subgroups of s4

Reference no: EM13179134

1. prove that for φ from R to R given by φ(x) = 2x is an automorphism of the reals under addition

2. is φ, when restricted to (R^+), an automorphism of the positive reals under multiplication? why?

3. What are the possible orders of subgroups of S4? Prove that S4 has at least one subgroup of each of these orders. What are the elements of these subgroups?

4. Prove or disprove that U(13) is isomorphic to U(21)

Reference no: EM13179134

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