OFFSET
1,2
COMMENTS
a(n) <= (n-1)^(n + (n-2)[log_2(n-1)]) for n > 4 [Ledermann, Neumann, Thm. 6.6].
a(n) is odd [MacHale, Sheehy, Thm. 15].
a(2n-1) = a(2n) for 1 < n < 204 [ibid.].
LINKS
John N. Bray and Robert A. Wilson, On the orders of automorphism groups of finite groups, Bull. London Math. Soc. 37 (2005) 381--385.
W. Ledermann, B. H. Neumann, On the order of the automorphism group of a finite group. I, Proc. Roy. Soc. Lon., 233A(1195) (1956), 494-506
D. MacHale and R. Sheehy, Finite groups with few automorphisms, Math. Proc. Roy. Irish Acad., 104A(2) (2004), 231--238.
Benjamin Sambale, On a theorem of Ledermann and Neumann, arXiv:1909.13220 [math.GR], 2019.
EXAMPLE
a(3) = a(4) = 7 because every finite group with at least 7 elements has at least 4 automorphisms while the cyclic group of order 6 has only phi(6)=2 automorphisms.
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Benoit Jubin, Apr 06 2008, May 26 2008
STATUS
approved