A cyclic group can be generated by a/an ________ element.ans.inversenon-singularmultiplicativesingular Previous Marked for Review Next

A cyclic group can be generated by a/an ________ element. ans. inverse singular non-singular multiplicative

A cyclic group can be generated by a/an ________ element.ans.

Every cyclic group is also a:a.Generatorb.Abelian groupc.Non-abelian groupd.Trivial group

What is a cyclic group?a.A group in which the binary operation is commutativeb.A group that contains only one elementc.A group in which every element can be generated by a single elementd.A group that does not have an identity element

Find explict automorphisms generating Aut(𝐶37 ) as a direct product of cyclic groups We know that the automorphism group of the cyclic group 𝐶37=⟨𝑥∣𝑥37=1⟩ is isomorphic to a direct product of cyclic groups. If 𝜙𝑟:𝐶37→𝐶37 is the homomorphism 𝑥↦𝑥𝑟 find a minimal list of generators for Aut(𝐶37)=⟨𝜙𝑟1,…,𝜙𝑟𝑡⟩ . (Your answer should be a set of one or more integers. For example if Aut(𝐶37)=⟨𝜙3,𝜙7⟩ then enter {3,7} .)