(4) This exercise outlines a proof that [21 KI 1//IIKİ whenever H and K are subgroups of a group ...
(4) This exercise outlines a proof that [21 KI 1//IIKİ whenever H and K are subgroups of a group G. (Note that HK-{hk | he H and k E K). The set HK is not always a subgroup of G.) Let -{hK | h є H). Define an action . . H x Ο Ο by the rule hị . ћК hihi. (You may assume that this is an action.)