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We prove a variant of the Titchmarsh convolution theorem for simply connectedsupersolvable Lie groups, namely we show that the convolution algebras ofcompactly supported continuous functions and compactly supported finitemeasures on such groups do not contain zero divisors. This can be also viewedas a topological version of the zero divisor conjecture of Kaplansky.

The problem of zero divisors in convolution algebras of supersolvable Lie groups