Cyclic groups

Related BrainMass Solutions

• Analysis of Cyclic Groups

  402858 Cyclic groups Describe what cyclic groups are and show that they are abelian. Describe their structure and the structure of their subgroups and factor groups up to isomorphism. A cyclic group is generated by an element of the group.

• Odd Order and Cyclic Groups

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• Symmetric Groups

  If S[n] is cyclic, then S[n] is generated by only one element. This is a contradiction. Thus S[n] can not be cyclic. Symmetric Groups are investigated.

• Factor Groups of Non-Abelian Groups

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• Cyclic Groups and Generators

  109246 Cyclic Groups and Generators Let G = be a cyclic group of size 600. What is a generator for the smallest subgroup of G that includes both a^42 and a^70? Since G is a cyclic group of size 600, we can assume that G=, where a^600=e.

• Cyclic Groups, Generators and Orders of Elements

  43681 Cyclic Groups, Generators and Orders of Elements (1) Let G be a group such that ... Show that G cannot be cyclic. (2) Show that a cyclic group with one generator has at most 2 elements.