Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On $ r$th roots in eighth-groups


Author: Spenser O. Gowdy
Journal: Proc. Amer. Math. Soc. 51 (1975), 253-259
MSC: Primary 20F05
DOI: https://doi.org/10.1090/S0002-9939-1975-0372045-7
MathSciNet review: 0372045
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be an eighth-group having no relators of the form $ R \cong {a^t}$. If $ {X^r} = {a^n}$ where $ a$ is a generator and $ X$ is a word then $ r$ divides $ n$ and $ X = {a^{n/r}}$.


References [Enhancements On Off] (What's this?)

  • [1] M. Dehn, Über unendliche diskontinuierlicke Gruppen, Math. Ann. 71 (1911), 116-144. MR 1511645
  • [2] -, Transformation der Kurven auf zweiseitigen Flächen, Math. Ann. 72 (1912), 413-421. MR 1511705
  • [3] M. D. Greendlinger, Dehn's algorithm for the word problem, Comm. Pure Appl. Math. 13 (1960), 67-83. MR 23 #A1693. MR 0124381 (23:A1693)
  • [4] -, On Dehn's algorithm for the conjugacy and word problems, with applications, Comm. Pure Appl. Math. 13 (1960), 641-677. MR 23 #A2327. MR 0125020 (23:A2327)
  • [5] Seymour Lipschutz, Elements in $ S$-groups with trivial centralizers, Comm. Pure Appl. Math. 13 (1960), 679-683. MR 23 #A2455. MR 0125149 (23:A2455)
  • [6] -, On square roots in eighth-groups, Comm. Pure Appl. Math. 15 (1962), 39-43. MR 29 #141. MR 0162837 (29:141)
  • [7] -, An extension of Greendlinger's results on the word problem, Proc. Amer. Math. Soc. 15 (1964), 37-43. MR 28 #4018. MR 0160808 (28:4018)
  • [8] -, Powers in eighth-groups, Proc. Amer. Math. Soc. 16 (1965), 1105-1106. MR 31 #5894. MR 0181667 (31:5894)
  • [9] -, On the conjugacy problem and Greendlinger's eighth-groups, Proc. Amer. Math. Soc. 23 (1969), 101-106. MR 40 #4343. MR 0251112 (40:4343)
  • [10] W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Pure and Appl. Math., vol. 13, Interscience, New York, 1966. MR 34 #7617. MR 0207802 (34:7617)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20F05

Retrieve articles in all journals with MSC: 20F05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0372045-7
Keywords: Finitely presented groups, generators and relators, Greendlinger's lemma, word problem, conjugacy problem, free groups, free products, small cancellation groups
Article copyright: © Copyright 1975 American Mathematical Society

American Mathematical Society