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

  Proof: We know, each element g in G can generate a cyclic group . So if the order of G is 2n+1, G contains at most 2n+1 cyclic subgroups. Now we want to show that G contains at most n+1 cyclic groups.

• Cyclic groups

  3746 Subgroups of cyclic groups Show that any subgroup of a cyclic group is cyclic. See attached PDF file. This si a proof regarding cyclic groups and subgroups.

• Cyclic groups

  The cyclic groups for modern algebra are examined.

• 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

  Therefore, G/Z(G) can not be cyclic. Factor Groups of Non-Abelian Groups are investigated.

• Group Theory : Symmetry Groups, Cyclic Subgroups and Permutations

  Symmetry Groups, Cyclic Subgroups and Permutations are investigated. The solution is detailed and well presented.

• 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.

• Orders of Cyclic Groups, Prime Order and Subgroups

  Orders of cyclic groups, prime order and subgroups are investigated. The solution is detailed and well presented.

• 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.