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Hello all,

I would like an explanation as to the structure description of the automorphism group of a Paley graph.

Paley graphs are a specific case of Cayley graphs where the group is $Z_q$ (q is a prime power for some prime p = 1 mod 4) and the connection set is all the quadratic residues in GF(q).

I'll be satisfied even with the less general case where q is prime.

I'm pretty sure that the said group is a semi-direct product of CyclicGroup(q) and CyclicGroup(q-1/2) but I have trouble showing it in the general case...

Thanks!

P.S

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# Automorphism Group of Paley Graph

Hello all,

I would like an explanation as to the structure description of the automorphism group of a Paley graph.

Paley graphs are a specific case of Cayley graphs where the group is $Z_q$ (q is a prime power for some prime p = 1 mod 4) and the connection set is all the quadratic residues in GF(q).

I'll be satisfied even with the less general case where q is prime.

I'm pretty sure that the said group is a semi-direct product of CyclicGroup(q) and CyclicGroup(q-1/2) but I have trouble showing it in the general case...

Thanks!