Abstract Algebra: Theory and Applications · Problem 4.5.3

Cyclic Groups — Thomas Judson

Mathematics — Abstract Algebra · cyclic-groups-subgroups

Problem

List all of the elements in each of the following subgroups. ((a)) The subgroup of

\mathbb{Z}

generated by

7

((b)) The subgroup of

\mathbb{Z}_{24}

generated by

15

((c)) All subgroups of

\mathbb{Z}_{12}

((d)) All subgroups of

\mathbb{Z}_{60}

((e)) All subgroups of

\mathbb{Z}_{13}

((f)) All subgroups of

\mathbb{Z}_{48}