Abstract Algebra: Theory and Applications · Problem 9.4.19

Normal Subgroups and Factor Groups — Thomas Judson

Mathematics — Abstract Algebra · direct-products-dihedral

Problem

Prove that

S_3 \times \mathbb{Z}_2

is isomorphic to

D_6

. Can you make a conjecture about

D_{2n}

? Prove your conjecture. Hint. Draw the picture.