Trace polynomial for two-generator subgroups of

Author:
Charles R. Traina

Journal:
Proc. Amer. Math. Soc. **79** (1980), 369-372

MSC:
Primary 10D40

DOI:
https://doi.org/10.1090/S0002-9939-1980-0567974-7

MathSciNet review:
567974

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Abstract: If *G* is a group generated by two matrices *A* and *B* having determinant , with entries from the complex field **C**, it is known that the trace of any word in *A* and *B*, is a polynomial with integral coefficients in the three variables: , defined as

*P*is determined uniquely by the conjugacy class of .

The actual computation of this trace polynomial is not easily obtained. It is the purpose of this paper to derive an explicit formula for this trace polynomial, and to indicate some consequences of it.

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DOI:
https://doi.org/10.1090/S0002-9939-1980-0567974-7

Article copyright:
© Copyright 1980
American Mathematical Society