A235388 Number of groups of order 2n generated by involutions.

1, 1, 1, 2, 1, 1, 1, 4, 2, 1, 1, 4, 1, 1, 1, 12, 1, 3, 1, 3, 1, 1, 1, 11, 2, 1, 4, 3, 1, 3, 1, 49, 1, 1, 1, 12, 1, 1, 1, 9, 1, 2, 1, 3, 2, 1, 1, 46, 2, 3, 1, 3, 1, 8, 1, 9, 1, 1, 1, 10, 1, 1, 2, 359, 1, 2, 1, 3, 1, 2, 1, 40, 1, 1, 3, 3, 1, 2, 1, 38, 11, 1, 1

Offset

1,4

Comments

a(n) >= A104404(n). This can be proved using the characterization in A104404. Given an Abelian group G, the semidirect product G : <h>, where h^2 = 1 and hgh = g^(-1) for any g in G, is generated by involutions. There is also a semidirect product Q8 : C2 generated by involutions. So an involution-generated group G : C2 exists for any finite group G that has all subgroups normal, and it can be shown that they are all nonisomorphic.

Links

Eric M. Schmidt, Table of n, a(n) for n = 1..511

Prog

(GAP)
IsInvolutionGenerated := G -> Group(Filtered(G, g->g^2=Identity(G)))=G;
A235388 := function(n) local i, count; count := 0; for i in [1..NrSmallGroups(2*n)] do if IsInvolutionGenerated(SmallGroup(2*n, i)) then count := count + 1; fi; od; return count; end;

Crossrefs

Sequence in context: A162510 A292589 A297404 * A294897 A252733 A181876

Adjacent sequences: A235385 A235386 A235387 * A235389 A235390 A235391

Keyword

nonn

Author

Eric M. Schmidt, Jan 08 2014

Status

approved