Which of the following is true? Choose one answer. a. Every group oforder 4 is c

Question

Which of the following is true? Choose one answer. a. Every group oforder 4 is cyclic
b. Every group oforder 4 is abelian
c. Every group oforder 4 is generated by a single element
d. There are aninfinite number of groups of order 4 Which of the following is true? Choose one answer. a. Every group oforder 4 is cyclic
b. Every group oforder 4 is abelian
c. Every group oforder 4 is generated by a single element
d. There are aninfinite number of groups of order 4 Choose one answer. a. Every group oforder 4 is cyclic
b. Every group oforder 4 is abelian
c. Every group oforder 4 is generated by a single element
d. There are aninfinite number of groups of order 4 Choose one answer. a. Every group oforder 4 is cyclic
b. Every group oforder 4 is abelian
c. Every group oforder 4 is generated by a single element
d. There are aninfinite number of groups of order 4

Explanation / Answer

There are only two non-isomorphic groups of order 4, thecyclic group of order 4 with one generator and the Klein -4 groupof order 4 with two generators. They are both abelian. The firstnon abelian group is of order 6 (symmetric group). Thus the answer is b.

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