Let p be an odd prime Prove that there are, at most, two nonabelian groups of order p 3 One has generators a,b satisfying a p 2 b p b 1 ab a i P the other has generators a,b,c satisfying a b c p c a 1 b 1 ab ca ac cb bc ...

We will show that the two given groups are the only possible nonabelian groups of order p3 First let G be a nonabelian group of order p3 By the class ...

Let p be an odd prime. Prove that there are, at most, two nonabelian groups of order

Question:

Let p be an odd prime. Prove that there are, at most, two nonabelian groups of order p³• [One has generators a,b satisfying |a| = p² ; |b|= p; b^-1ab = a^i+P; the other has generators a,b,c satisfying |a| = |b| = |c| = p; c = a^-1b^-1ab; ca = ac; cb = bc.]

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