Let G be a group of order n. For what value of n is the group G NOT cyclic?
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Let G be a group of order n. For what value of n is the group G NOT cyclic?
Select one:
a.
n=10
b.
n=15
c.
n=35
d.
n=17
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- Find the order of each of the following elements in the multiplicative group of units . for for for forThe alternating group A4 on 4 elements is the same as the group D4 of symmetries for a square. That is. A4=D4.Exercises 8. Let be an element of order in a group. Find the order of each of the following. a. b. c. d. e. f. g. h.
- Exercises 7. Let be an element of order in a group. Find the order of each of the following. a. b. c. d. e. f. g.Exercises 13. For each of the following values of, find all subgroups of the group described in Exercise, addition and state their order. a. b. c. d. e. f.Exercises 21. Suppose is a cyclic group of order. Determine the number of generators of for each value of and list all the distinct generators of . a. b. c. d. e. f.
- 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,,,, }.Let G= a be a cyclic group of order 35. List all elements having each of the following orders in G. a. 2 b. 5 c. 7 d. 10Que 327: Let X, Y be cyclic groups of order 2,3 respectively. Find the orders of the elements of X XY.
- List all the groups of order 17. You must justify your answer.How many subgroups of the group G = (Z30, +30)? a. 8 O b. 6 C. 5 O d. 7 е. 4Let G be a group of order 3 and identity e. If the other elements are a and b, use the Latin square property to draw up the group table for G, and deduce that a3 = e