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A235388 Number of groups of order 2n generated by involutions. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 17:12 EST 2021. Contains 349424 sequences. (Running on oeis4.)