Polynomial maps and polynomial sequences in groups
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Ya-Qing Hu
Abstract
This paper presents a modified version of Leibman’s group-theoretic generalizations of the difference calculus for polynomial maps from nonempty commutative semigroups to groups, and proves that it has many desirable formal properties when the target group is locally nilpotent and also when the semigroup is the set of nonnegative integers. We will apply it to solve Waring’s problem for general discrete Heisenberg groups in a sequel to this paper.
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1401419
Funding statement: This work was partially supported by NSF Grant grant number DMS-1401419 and the Postdoctoral International Exchange Program of the China Postdoctoral Council grant number YJ20210319.
Acknowledgements
I thank my advisor Michael Larsen for the guidance and many helpful discussions through this work, in particular, for bringing this problem to my attention. Also, I thank the anonymous referee for many helpful references and comments that improved the quality of this work.
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Communicated by: Benjamin Klopsch
References
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Articles in the same Issue
- Frontmatter
- Multiple transitivity except for a system of imprimitivity
- Realizing finite groups as automizers
- Action of automorphisms on irreducible characters of finite reductive groups of type 𝖠
- Polynomial maps and polynomial sequences in groups
- Units, zero-divisors and idempotents in rings graded by torsion-free groups
- The algebraic entropy of one-dimensional finitary linear cellular automata
- Sublinearly Morse boundary of CAT(0) admissible groups
Articles in the same Issue
- Frontmatter
- Multiple transitivity except for a system of imprimitivity
- Realizing finite groups as automizers
- Action of automorphisms on irreducible characters of finite reductive groups of type 𝖠
- Polynomial maps and polynomial sequences in groups
- Units, zero-divisors and idempotents in rings graded by torsion-free groups
- The algebraic entropy of one-dimensional finitary linear cellular automata
- Sublinearly Morse boundary of CAT(0) admissible groups
