let G = D2n =
{e,r,r^2,...,rn-1,s,sr,sr2,..,srn-1}
a diedergroup of order 2n, where n >=3
(a) prove that [G,G]...
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let G = D2n ={e,r,r^2,...,rn-1,s,sr,sr2,..,srn-1}a diedergroup of order 2n, where n >=3 (a) prove that [G,G] = 2> (b) prove that G/[G,G] consists of two elements if n is uneven and4 elements if n is even
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The proof for a is provided as follows First we show that every element of the cyclic group is a commutator1 and later we show that every commutator of G is in the group 2 so that 1 and 2 completes the proof So let us start with the proof of the fact 1The commutator rs is defined as rsr1s1 which equals rrss1 REASON In any
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