On $r$th roots in eighth-groups
HTML articles powered by AMS MathViewer
- by Spenser O. Gowdy PDF
- Proc. Amer. Math. Soc. 51 (1975), 253-259 Request permission
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
- M. Dehn, Über unendliche diskontinuierliche Gruppen, Math. Ann. 71 (1911), no. 1, 116–144 (German). MR 1511645, DOI 10.1007/BF01456932
- M. Dehn, Transformation der Kurven auf zweiseitigen Flächen, Math. Ann. 72 (1912), no. 3, 413–421 (German). MR 1511705, DOI 10.1007/BF01456725
- Martin Greendlinger, Dehn’s algorithm for the word problem, Comm. Pure Appl. Math. 13 (1960), 67–83. MR 124381, DOI 10.1002/cpa.3160130108
- Martin Greendlinger, On Dehn’s algorithms for the conjugacy and word problems, with applications, Comm. Pure Appl. Math. 13 (1960), 641–677. MR 125020, DOI 10.1002/cpa.3160130406
- Seymour Lipschutz, Elements in $S$-groups with trivial centralizers, Comm. Pure Appl. Math. 13 (1960), 679–683. MR 125149, DOI 10.1002/cpa.3160130407
- Seymour Lipschutz, On square roots in eighth-groups, Comm. Pure Appl. Math. 15 (1962), 39–43. MR 162837, DOI 10.1002/cpa.3160150103
- Seymour Lipschutz, An extension of Greendlinger’s results on the word problem, Proc. Amer. Math. Soc. 15 (1964), 37–43. MR 160808, DOI 10.1090/S0002-9939-1964-0160808-5
- Seymour Lipschutz, Powers in eighth-groups, Proc. Amer. Math. Soc. 16 (1965), 1105–1106. MR 181667, DOI 10.1090/S0002-9939-1965-0181667-1
- Seymour Lipschutz, On the conjugacy problem and Greendlinger’s eighth-groups, Proc. Amer. Math. Soc. 23 (1969), 101–106. MR 251112, DOI 10.1090/S0002-9939-1969-0251112-X
- Wilhelm Magnus, Abraham Karrass, and Donald Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Interscience Publishers [John Wiley & Sons], New York-London-Sydney, 1966. MR 0207802
Additional Information
- © Copyright 1975 American Mathematical Society
- 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