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Register a new userAlgebraic Semigroups are Strongly {pi}-regular
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Let $S$ be an algebraic semigroup (not necessarily linear) defined over a field $F$. We show that there exists a positive integer $n$ such that $x^n$ belongs to a subgroup of $S(F)$ for any $x in S(F)$. In particular, the semigroup $S(F)$ is strongly {pi}-regular.
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We prove that an analogue of Jordans theorem on finite subgroups of general linear groups holds for the groups of biregular automorphisms of algebraic surfaces. This gives a positive answer to a question of Vladimir L. Popov.
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