Reading Question 6.3.4. Let G = (g) be a cyclic group of order n. Which of the following claims is true? Select all that apply. (a) The number of "nodes" in the subgroup diagram of G is equal to p(n) (i.e., the number of integers 1

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Reading Question 6.3.4. Let G = (g) be a cyclic group
of order n.
Which of the following claims is true? Select all that apply.
(a) The number of "nodes" in the subgroup diagram of G is equal to p(n) (i.e., the number of
integers 1 <k < n that are coprime with n).
(b) The number of "nodes" in the subgroup diagram of G is equal the number of positive divisors
of n.
(c) If n = pk with p prime and k E N, then the subgroup diagram of G looks like a straight line.
(d) If n
p
where p and
q are two distinct primes, then the subgroup diagram of G has exactly 4
nodes and 4 line segments.
Transcribed Image Text:Reading Question 6.3.4. Let G = (g) be a cyclic group of order n. Which of the following claims is true? Select all that apply. (a) The number of "nodes" in the subgroup diagram of G is equal to p(n) (i.e., the number of integers 1 <k < n that are coprime with n). (b) The number of "nodes" in the subgroup diagram of G is equal the number of positive divisors of n. (c) If n = pk with p prime and k E N, then the subgroup diagram of G looks like a straight line. (d) If n p where p and q are two distinct primes, then the subgroup diagram of G has exactly 4 nodes and 4 line segments.
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