[GAP Forum] FAWAD ALI M.Phil (Pure Mathematics) 3rd semester scholar From Pakistan,

[Fawad Hayat]

Hello sir,
sir I have a problem that how to write a command in GAP the automorphism
group of finite abelian group and their fixed points.
Let Z_pXZ_q be cyclic group where p & q are distinct primes,
Let suppose p=2 & q=3
=>  G:=Z_2XZ_3= {(0,0),(0,1),(0,2),(1,0),(1,1),(1,2)}
be a cyclic group, and 'd' is the divisor of the order of a group G  i.e (
d/IGI  =>d=1,2,3,6)
how to list all the automorphisms of a group Aut(G), and how to find
explicitly all those automorphisms  fixing 'd' elements, where fix means
f(x)=x ; for some x belongs to G & for f belongs to Aut(G).
f(e)=e : by homomorphism property,

i.e  For d=1,
A={set of all those automorphisms of Aut(G) fixing d=1 element only (
Identity element)}
For d=2,
B={set of all those automorphisms of Aut(G) fixing d=2 element}
For d=3
C={set of all those automorphisms of Aut(G) fixing d=3 element}
For d=6
D={ I : because identity is the only auto fixing all the elements of a
group G }

Sir, I need The command which gives me the complete calculation from GAP
Thanks Sir,
Regards FAWAD ALI From pakistan