|
| |
|
|
A090130
|
|
Number of groups of order 5^n.
|
|
8
|
| |
|
|
|
OFFSET
|
0,3
|
|
|
REFERENCES
|
G. Bagnera, La composizione dei Gruppi finiti il cui grado e la quinta potenza di un numero primo, Ann. Mat. Pura Appl. (3), 1 (1898), 137-228.
Hans Ulrich Besche, Bettina Eick and E. A. O'Brien, A Millennium Project: Constructing Small Groups, International Journal of Algebra and Computation, Vol. 12, No 5 (2002), 623-644.
W. Burnside, Theory of Groups of Finite Order, Dover, NY, 1955.
|
|
|
LINKS
|
Table of n, a(n) for n=0..7.
M. F. Newman, E. A. O'Brien and M. R. Vaughan-Lee, Groups and nilpotent Lie rings whose order is the sixth power of a prime, J. Algebra, 278 (2004), 383-401.
E. A. O'Brien and M. R. Vaughan-Lee, The groups of order p^7 for odd prime p, J. Algebra 292, 243-258, 2005. [Eamonn O'Brien, Mar 06 2010]
|
|
|
FORMULA
|
For a prime p >= 5, the number of groups of order p^n begins 1, 1, 2, 5, 15, 61 + 2*p + 2*gcd (p - 1, 3) + gcd (p - 1, 4), 3*p^2 + 39*p + 344 + 24*gcd(p - 1, 3) + 11*gcd(p - 1, 4) + 2*gcd(p - 1, 5), ...
|
|
|
PROG
|
(GAP) A090130 := List([0..7], n -> NumberSmallGroups(5^n)); # Muniru A Asiru, Oct 15 2017
|
|
|
CROSSREFS
|
Cf. A000001, A000679, A090091, A090140.
Sequence in context: A090091 A268122 A133645 * A090140 A032267 A191477
Adjacent sequences: A090127 A090128 A090129 * A090131 A090132 A090133
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Eamonn O'Brien (obrien(AT)math.auckland.ac.nz), Jan 22 2004
|
|
|
EXTENSIONS
|
Corrected and extended by David Radcliffe, Feb 24 2010
Corrected and extended by Eamonn O'Brien, Mar 06 2010
|
|
|
STATUS
|
approved
|
| |
|
|
