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)

 
 

 

Combinatorial equivalence between group presentations


Author: Sushil Jajodia
Journal: Proc. Amer. Math. Soc. 85 (1982), 165-168
MSC: Primary 20E06; Secondary 20F05
DOI: https://doi.org/10.1090/S0002-9939-1982-0652434-7
MathSciNet review: 652434
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ \mathcal{P} = ({x_1}, \ldots ,{x_n}:{W_1}, \ldots ,{W_m})$ and $ \mathcal{R} = ({x_1}, \ldots ,{x_n}:{R_1}, \ldots ,{R_m})$ be two presentations, with the same generators, for a group $ \pi $. In this note, we give a necessary and sufficient criterion which insures the existence of a combinatorial equivalence between $ \mathcal{P}$ and $ \mathcal{R}$ requiring only replacement operations.


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

  • [1] J. S. Birman, An inverse function theorem for free groups, Proc. Amer. Math. Soc. 41 (1973), 634-638. MR 0330295 (48:8632)
  • [2] R. H. Fox, Free differential calculus. I. Derivation in the free group ring, Ann. of Math. (2) 57 (1953), 547-560. MR 0053938 (14:843d)
  • [3] W. Magnus, A. Karrass and D. Solitar, Combinatorial group theory, Interscience, New York, 1966.
  • [4] J. McCool and A. Pietrowski, On free products with amalgamation of two infinite cyclic groups, J. Algebra 18 (1971), 377-383. MR 0280576 (43:6296)
  • [5] W. Metzler, Über den homotopietyp zweidimensionaler $ CW$-Komplexes und Elementartransformationen bei definierende relatumen, J. Reine Angew. Math. 285 (1976), 7-23. MR 0440527 (55:13402)
  • [6] M. S. Montgomery, Left and right inverses in group algebras, Bull. Amer. Math. Soc. 75 (1969), 539-540. MR 0238967 (39:327)
  • [7] E. S. Rapaport, Groups of order 1: Some properties of presentations, Acta Math. 121 (1968), 127-150. MR 0229704 (37:5278)
  • [8] A. J. Sieradski, Combinatorial isomorphisms and combinatorial homotopy equivalences, J. Pure Appl. Algebra 7 (1976), 59-95. MR 0405434 (53:9227)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20E06, 20F05

Retrieve articles in all journals with MSC: 20E06, 20F05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0652434-7
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society