Let H be a subgroup of a group G and a, be G. Then be aH if and only if None of these O ab e H O ab-1 e H а-1b € H

Q: Let a and b be elements of a group G and H and K be subgroups ofG. If aH = bK, prove that H = K.

A: Given: a and b are the elements of  group G and H respectively and K is a subgroup of G. To Do: If…

Q: Let a and b be elements of a group.  If |a| and |b| are relatively prime, show that intersects =…

A: Let m and n be the order of the elements a and b of a group G. Given that the orders of a and b are…

Q: (1).* 4 and |6| = 2, Let G be a group. Let a, b EG such that |a| and a b = ba. Then determine |ba|,…

A:

Q: Decide if each of the following sets H is a subgroup or not of the group G = R XR, where the group…

A:

Q: Let H and K be subgroups of a group G and assume |G : H| = +0. Show that |K Kn H |G HI if and only…

A: Given:

Q: disprove: If G is a group and H, K < G are two subgroups, then (HK)≤ G.

A: