Consider the group Z × Z under * such that
(a, b) * (c, d) = (a + c, b + d).
(here + means + is in Z and + is in Z)
We would like to find a group of permutations that is isomorphic to ZZ.
Is this group cyclic? If so, prove it. If not, explain why.
Let a=(1 2 3 4) and b=(5 6 7 8 9 10) be two cycles in the permutation
group S10. a and b are two disjoint cycles. Let G=<a,b> be the subgroup
generated by a and b.
Now I show that G is isomorphic to Z4xZ6.
Since a and b are disjoint, then ab=ba. So each ...
Isomorphisms, Cyclic Groups and Groups of Permutations are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.