|
|
A090751
|
|
Number of indecomposable groups of order n.
|
|
8
|
|
|
0, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 0, 8, 1, 2, 1, 2, 1, 1, 1, 6, 1, 1, 3, 1, 1, 1, 1, 34, 0, 1, 0, 4, 1, 1, 1, 5, 1, 2, 1, 1, 0, 1, 1, 23, 1, 2, 0, 2, 1, 6, 1, 5, 1, 1, 1, 3, 1, 1, 1, 201, 0, 1, 1, 2, 0, 1, 1, 19, 1, 1, 1, 1, 0, 2, 1, 24, 9, 1, 1, 3, 0, 1, 0, 4, 1, 2, 0, 1, 1, 1, 0, 121, 1, 2, 0, 6, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,8
|
|
COMMENTS
|
Indecomposable means nontrivial and not a direct product of two proper subgroups. Any finite group G is a direct product of indecomposable groups and the multiset of isomorphism types of indecomposable factors is an invariant of G. Hence A000001 has Dirichlet generating function Product_{n>=2} (1 - n^(-s))^(-a(n)).
|
|
REFERENCES
|
Derek J. S. Robinson, A course in the theory of groups, Graduate texts in mathematics 80, Springer-Verlag, 1982.
|
|
LINKS
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,nice
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|