Abstract Algebra: Theory and Applications · Problem 9.4.22

Normal Subgroups and Factor Groups — Thomas Judson

Mathematics — Abstract Algebra · internal-direct-products

Problem

Let

G

be a group of order 20. If

G

has subgroups

H

and

K

of orders 4 and 5 respectively such that

hk = kh

for all

h \in H

and

k \in K

, prove that

G

is the internal direct product of

H

and

K