cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A060938 Maximal degree of an irreducible representation of a group with n elements.

This page as a plain text file.
%I A060938 #4 Oct 17 2012 13:52:46
%S A060938 1,1,1,1,1,2,1,2,1,2,1,3,1,2,1,2,1,2,1,4,3,2,1,3,1,2,3,2,1,2,1,4,1,2,
%T A060938 1,4,1,2,3,4,1,6,1,2,1,2,1,4,1,2,1,4,1,6,5,7,3,2,1,5,1,2,3,4,1,2,1,4,
%U A060938 1,2,1,8,1,2,3,2,1,6,1,5,3,2,1,6,1,2,1
%N A060938 Maximal degree of an irreducible representation of a group with n elements.
%C A060938 a(n) = 1 iff every group of order n is Abelian i.e. n belongs to sequence A051532.
%C A060938 a(m)a(n) <= a(mn). - _Eric M. Schmidt_, Oct 17 2012
%H A060938 Eric M. Schmidt, <a href="/A060938/b060938.txt">Table of n, a(n) for n = 1..1535</a>
%e A060938 a(6) = 2 because for the Abelian group with 6 elements the degrees are all 1 and for the symmetric group S_3 the degrees are 1,1,2.
%o A060938 (GAP) A060938 := function(n) local max, divs, maxpos, degs, i; if (n=1) then return 1; fi; divs := DivisorsInt(n); maxpos := divs[Int(Length(divs)/2)]; max := 1; for i in [1..NumberSmallGroups(n)] do degs := CharacterDegrees(SmallGroup(n, i)); max := Maximum(max, degs[Length(degs)][1]); if (max = maxpos) then return max; fi; od; return max; end;
%Y A060938 Cf. A051532.
%K A060938 nonn
%O A060938 1,6
%A A060938 Ahmed Fares (ahmedfares(AT)my-deja.com), May 07 2001
%E A060938 More terms from _Eric M. Schmidt_, Oct 17 2012