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
KEYWORD
nonn
AUTHOR
Eric M. Schmidt, Jan 08 2014
STATUS
approved