This article is about a GAP function.
This GAP function is not in-built: you need to copy the code on this page to define the function.
The function takes two arguments, both of which are positive integers, and outputs a boolean variable (true/false).
The goal is to take inputs and , with a positive integer and a prime power, and output the special affine group .
The current version works only when the prime power is itself a prime number.
SA := function(n,q) local A,B,C; if (q = 2 and n = 2) then return SymmetricGroup(4); fi; if IsPrime(q) then A := ElementaryAbelianGroup(q^n); B := AutomorphismGroup(A); C := DerivedSubgroup(B); return SemidirectProduct(C,A); else if IsPrimePower(q) then Print("Method not yet available for prime powers other than primes\n"); fi; fi; end;;