Academic Journal
A Tits alternative for endomorphisms of the projective line.
| Τίτλος: | A Tits alternative for endomorphisms of the projective line. |
|---|---|
| Συγγραφείς: | Bell, Jason P., Keping Huang, Wayne Peng, Tucker, Thomas J. |
| Πηγή: | Journal of the European Mathematical Society (EMS Publishing); 2024, Vol. 26 Issue 12, p4903-4922, 20p |
| Θεματικοί όροι: | Endomorphisms, Semigroup algebras, Nonabelian groups, Semigroups (Algebra), Program generators (Computer programs) |
| Περίληψη: | We prove an analog of the Tits alternative for endomorphisms of P1. In particular, we show that if S is a finitely generated semigroup of endomorphisms of P1 over C, then either S has polynomially bounded growth or S contains a nonabelian free semigroup. We also show that if f and g are polarizable maps over any field of any characteristic and Prep.f / 6D Prep.g/, then for all sufficiently large j, the semigroup hf j; gj i is a free semigroup on two generators. [ABSTRACT FROM AUTHOR] |
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| Βάση Δεδομένων: | Complementary Index |
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