Abstract Algebra: Theory and Applications · Problem 11.4.7

Matrix Groups and Symmetry — Thomas Judson

Mathematics — Abstract Algebra · second-isomorphism-theorem

Problem

In the group

\mathbb{Z}_{24}

, let

H = \langle 4 \rangle

and

N = \langle 6 \rangle

. (a) List the elements in

HN

(we usually write

H + N

for these additive groups) and

H \cap N

. (b) List the cosets in

HN/N

, showing the elements in each coset. (c) List the cosets in

H/(H \cap N)

, showing the elements in each coset. (d) Give the correspondence between

HN/N

and

H/(H \cap N)

described in the proof of the Second Isomorphism Theorem.