Cyclic group

Related BrainMass Solutions

• Analysis of Cyclic Groups

  Any subgroup or factor group of a cyclic group is cyclic. If a group G has order n, and A is a subgroup of G, then the order of A must be a divisor of n.

• Homomorphism of cyclic group

  31108 Homomorphism of cyclic group Let G be a group and h:G-->h(G) a homomorphism.Prove or Disprove If G is cyclic,then h(G)is cyclic. This is true. Proof: Since G is cyclic, then G= for some a in G. Let h(a)=b in h(G).

• Group Theory : Cayley Tables, Cyclic Groups and Isomorphisms

  31559 Group Theory : Cayley Tables, Cyclic Groups and Isomorphisms ? I have the following cayley tables (which is in modulo 9) determine the order of each element . Prove that G is a cyclic group. ?

• Cyclic groups

  group Prove that every subgroup H of a cyclic group G = is itself cyclic See attached PDF file.

• 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.

• Prove that a cyclic group of prime order p has no non-trivial subgroups.

  97560 Prove that a cyclic group of prime order p has no non-trivial subgroups. Prove that a cyclic group of prime order p has no non-trivial subgroups. Let G = be a cyclic group of order p, where p is prime.

• Factor Groups of Non-Abelian Groups

  But now if it is not abelian, can we simply say because G is not cyclic, then any factor group will not be cyclic either? or is there more to it? Proof: If the factor group G/Z(G) is cyclic, then G/Z(G)= for some g in G.

• Group Theory : Symmetry Groups, Cyclic Subgroups and Permutations

  (a) Explain why this group has cyclic subgroups of order 1,2,3,4,5 and 6, and give examples of each of these. Explain why this group does not have cyclic subgroups of any other order.

• 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.

• Continuous Maps, Homomorphisms and Cyclic Groups

  How exactly does "there is a unique integer d such that..." follow from "H~_n (S^n) is an infinite cyclic group"? Call H~_n(S^n) G for short. Take a generator g of the group G, so G = {1, g, g^2, g^3 ,...., g^{-1}, g^{-2},... }.