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I am somewhat confused by the output from the AbelianInvariants function,

as applied to a finitely generated abelian group. I am using GAP 3.2

with upgrades 1 and 2, on a DEC Ultrix workstation, if it matters. In the

example below, I hoped to get the output [0 0], corresponding to the fact

that the abelianization of the free group on two letters ("a" and "b" below)

is Z+Z. Have I misused the function or misinterpreted the output?

Daniel Ruberman

ruberman@binah.cc.brandeis.edu

gap> a:=AbstractGenerator("a"); a gap> b:=AbstractGenerator("b"); b gap> G:=Group(a,b); Group( a, b ) gap> G.relators:=[]; [ ] gap> H:=CommutatorFactorGroup(G); Group( c.1, c.2 ) gap> H.relators; [ c.1^-1*c.2^-1*c.1*c.2 ] gap> AbelianInvariants(H); [ 0 ]

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