Consider the subgroup H={R0,R180} of D6. List the elements of the factor group D6/H.

Expert Solution

Recall , where < > denotes the group generated by. Note that we can identify , Thus the group H becomes . Thus we need to find the group . Note that , and , hence . Note in the group , , thus , , , . Hence the elements , , , will collapse in the group . Hence the group , where `bar' denotes going modulo H.

Now note that in the group we can identify .

Colby Messinger answered 2 years ago

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Question

Consider the subgroup H={R0,R180} of D6. List the elements of the factor group D6/H.

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