OFFSET
1,3
COMMENTS
LINKS
C. J. Hillar and D. L. Rhea, Automorphisms of finite abelian groups, arXiv:math/0605185 [math.GR], 2006.
C. J. Hillar and D. L. Rhea, Automorphisms of finite abelian groups, Amer. Math. Monthly 114 (2007), no 10, 917-923.
D. MacHale and R. Sheehy, Finite groups with few automorphisms, Math. Proc. Roy. Irish Acad., 104A(2) (2004), 231--238.
EXAMPLE
The table begins as follows:
1
1
2
2 6
4
2
6
4 8 168
6 48
4
10
4 12
The first row with two numbers corresponds to the two Abelian groups of order 4, the cyclic group C_4 and the Klein group C_2 x C_2, whose automorphism groups are respectively the group (C_4)^x = C_2 and the symmetric group S_3.
PROG
(GAP4)
Print("\n") ;
for o in [ 1 .. 40 ] do
n := NumberSmallGroups(o) ;
og := [] ;
for i in [1 .. n] do
g := SmallGroup(o, i) ;
if IsAbelian(g) then
H := AutomorphismGroup(g) ;
ho := Order(H) ;
Add(og, ho) ;
fi ;
od;
Sort(og) ;
Print(og) ;
Print("\n") ;
od; # R. J. Mathar, Jul 13 2013
CROSSREFS
KEYWORD
easy,nonn,tabf
AUTHOR
Benoit Jubin, May 12 2008
STATUS
approved