- #1
chibulls59
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Suppose K= < x > is a cyclic group with 2 elements and H= S3 is symmetric group with 6 elements. Find all different cyclic subgroups of G= H x K.
Now since K is generated by x with 2 elements, I have K= {1,x} and H= {1, (12), (13), (23), (123), (132)}
What I am confused about is finding cyclic subgroups of H x K. Am I supposed to be checking each element of H x K and seeing if it can generate the whole group?
Now since K is generated by x with 2 elements, I have K= {1,x} and H= {1, (12), (13), (23), (123), (132)}
What I am confused about is finding cyclic subgroups of H x K. Am I supposed to be checking each element of H x K and seeing if it can generate the whole group?