Suppose that a group G has order 8, but is not cyclic. Then that g for all g e G Select one: а. 1 3 b. g c. We cant know 2 d. g

Let A={ a,b,c }. Prove or disprove that P(A) is a group with respect to the operation of union. (Sec. 1.1,7c)

Find the right regular representation of G as defined Exercise 11 for each of the following groups. a. G={ 1,i,1,i } from Example 1. b. The octic group D4={ e,,2,3,,,, }.

Exercises 9. For each of the following values of, find all distinct generators of the cyclic group under addition. a. b. c. d. e. f.

Exercises 10. For each of the following values of, find all subgroups of the cyclic group under addition and state their order. a. b. c. d. e. f.

For each of the following values of n, find all distinct generators of the group Un described in Exercise 11. a. n=7 b. n=5 c. n=11 d. n=13 e. n=17 f. n=19

Find all subgroups of the octic group D4.

The alternating group A4 on 4 elements is the same as the group D4 of symmetries for a square. That is. A4=D4.

49. Find the multiplicative inverse of in the given group. a. b.

Exercises 30. For an arbitrary positive integer, prove that any two cyclic groups of order are isomorphic.