Idempotent-Conjugate Monoids with Nilpotent Unit Groups |
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Authors: | Mohan S Putcha |
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Institution: | (1) Department of Mathematics, Box 8205, North Carolina State University, Raleigh, NC 27695-8205, USA |
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Abstract: | Let M be a finite monoid with unit group G such that J-related
idempotents in M are conjugate. If G is nilpotent, we prove that the complex
monoid algebra CM of M is semisimple if and only if M is an inverse
monoid. Conversely let G be a finite group such that for any finite
idempotent-conjugate monoid M with unit group G, CM semisimple implies
that M is an inverse monoid. We then show that G is a nilpotent group. |
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