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A060938
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Maximal degree of an irreducible representation of a group with n elements.
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1
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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, 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, 1, 2, 1, 8, 1, 2, 3, 2, 1, 6, 1, 5, 3, 2, 1, 6, 1, 2, 1
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OFFSET
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1,6
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COMMENTS
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a(n) = 1 iff every group of order n is Abelian i.e. n belongs to sequence A051532.
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LINKS
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EXAMPLE
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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.
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PROG
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(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;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Ahmed Fares (ahmedfares(AT)my-deja.com), May 07 2001
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EXTENSIONS
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STATUS
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approved
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