Growth Rate on Finitely Generated Abelian Groups
- 발행기관 서강대학교 일반대학원
- 지도교수 이종범
- 발행년도 2015
- 학위수여년월 2015. 2
- 학위명 석사
- 학과 및 전공 일반대학원 수학과
- 실제URI http://www.dcollection.net/handler/sogang/000000055206
- 본문언어 영어
- 저작권 서강대학교 논문은 저작권보호를 받습니다.
초록/요약
The purpose of this paper is to study the growth rate of an endomorphism on a finitely generated group. We study that the growth rate is independent of the choice of a finite set of generators for a group, and the limit in its definition exists. We also study the fundamental-group growth rate which is a topological counter-part of the growth rate on finitely generated groups. We review some known facts about the growth rate, filling in some skipped part of the proofs in the standard reference [8]. We prove that the fundamental-group growth rate is a homotopy type invariant. We provide an example, showing a known result, [3, Theorem 3.1], is not correct. We prove that under a mild restriction this result and its proof are valid. When the group is finitely generated free Abelian, we prove a computation formula for the growth rate in the final section. This fact is already known, but to the best of our knowledge, its detailed proof cannot be found in the literature. We provide its proof, together with some examples.
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