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 A090130 Number of groups of order 5^n. 8
 1, 1, 2, 5, 15, 77, 684, 34297 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified March 28 08:48 EDT 2023. Contains 361584 sequences. (Running on oeis4.)