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A066389
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Number of 2-generated groups of order n: groups that have a generating set of size <=2, i.e., are cyclic or of the form <a,b>.
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3
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1, 1, 1, 2, 1, 2, 1, 4, 2, 2, 1, 5, 1, 2, 1, 9, 1, 4, 1, 5, 2, 2, 1, 13, 2, 2, 4, 4, 1, 4, 1, 20, 1, 2, 1, 12, 1, 2, 2, 12, 1, 6, 1, 4, 2, 2, 1, 35, 2, 4, 1, 5, 1, 10, 2, 11, 2, 2, 1, 13, 1, 2, 4, 54, 1, 4, 1, 5, 1, 4, 1, 37, 1, 2, 3, 4, 1, 6, 1, 35, 10, 2, 1
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OFFSET
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1,4
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LINKS
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PROG
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(GAP)
IsTwoGenerated := function(G) if IsSolvableGroup(G) then return (Length(MinimalGeneratingSet(G)) <= 2); fi; return ForAny(List(ConjugacyClasses(G), Representative), g->ForAny(G, h->Size(Group(g, h)) = Size(G))); end; A066389 := function(n) local count, i; count := 0; for i in [1..NumberSmallGroups(n)] do if IsTwoGenerated(SmallGroup(n, i)) then count := count + 1; fi; od; return count; end; # Eric M. Schmidt, May 02 2013; shortened by Eric M. Schmidt, May 20 2013
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CROSSREFS
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KEYWORD
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nonn,nice
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AUTHOR
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Sharon Sela (sharonsela(AT)hotmail.com), Dec 23 2001
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EXTENSIONS
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STATUS
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approved
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