Reading Question 5.3.3. Let G be a group and let g E G be an element of infinite order. Which of the following claims is true? Select all that apply. (a) g° = e. (b) g" + e for all n EZ (that is, no power of g is equal to the identity). (c) If g" = e for some n E Z, then n = 0. (d) G = 0.

with details

3.2 3.3 3.4 Consider the group (Z8, +(mod8)). a) List the elements of (Zg, +(mod8)). b) Find all the distinct left cosets of H = (2) in Zg. Let σ = (1,4,3,5) € S5, find σ-1 Find the order of a = (1,4,3,2) = S4.

Only 7.7 please.