Question

Find the first derived subgroup of D4?
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Answer 1

❤AnSwEr :-

The proper normal subgroups of D4 = {e, r, r2,r3, s, rs, r2s, r3s} are {e, r, r2,r3}, {e, r2, s, r2s}, {e, r2, rs, r3s}, and {e, r2}. To see this note that s is conjugate to r2s (conjugate by r), so if a subgroup contains s for it to be normal it must contain r2s.

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