GAP:SA

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.

Definition

Function type

The function takes two arguments, both of which are positive integers, and outputs a boolean variable (true/false).

Behavior

The goal is to take inputs $n$ and $q$, with $n$ a positive integer and $q$ a prime power, and output the special affine group $SA(n,q)$.

Code

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;;