One of the longstanding
problems in the the theory of infinite group algebras is the zero divisor conjecture:
does the group algebra of a torsion free group have zero divisors?
Results presented here grew out of an attempt to settle the conjecture for
abelian-by-finite groups. Since the problem is not solved it seems valuable to collect
in one paper most of the information about this case.
The conjecture has been verified for some limited classes of groups ([9], [8],
[5]).
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