Give an example,with justification,of a group G with subgroups H and K such that HK is not a subgroup of G.?

1 Answer
Feb 25, 2018

Here's an example...

Explanation:

Let #G = < a, b ># be the free group on two generators.

Let #H = < a ># be the subgroup generated by #a#

Let #K = < b ># be the subgroup generated by #b#

Then:

#HK = { a^m b^n | m, n in ZZ }#

#ab in HK#

#(ab)^(-1) = b^(-1) a^(-1) !in HK#