Sifat-Sifat Generator Modul Homotopi Kedua Dengan Menggunakan Transformasi Nielsen

Y. Yanita, Abdul Ghafur Ahmad

Abstract


Abstract. This paper discuss about relation the second homotopy module related to two different presentations which defining the same group.  These presentations can be transformed each other using Nielsen transformation methods.  This method only modifying its relator.  We consider the generators of second homotopy module after using Nielsen transformations.

Keyword : second homotopy module, Nielsen transformations, generators.


References


W. A. Bogley, S.J. Pride,: Calculating generator of , in wo-dimensional homotopy and combinatorial group theory (Hog-Angeloni, C., Metzler, W., Sieradski, A.J., eds.), CUP, 157 – 188 (1993).

Y. G. Baik, J. Harlander, S.J.Pride, The geometry of group extensions, J. Group Theory 1 (1998) 395 – 416.

C. Hog-Angeloni, W. Metzler. 1993. Geometric aspects of two-dimensional complexes. In Two-dimensional homotopy and combinatorial group theory (eds. C. Hog-Angeloni, W. Metzler and A. J. Sieradski), London Math. Soc. Lecture Note Ser. No. 197 (Cmbridge University Press), pp. 1 – 44.

S. Jajodia, Combinatorial equivalence between group presentations, Proceeding of the American Mathematical Society, Vol. 85, No. 2, (1982) 165 – 168.

W. Magnus, A. Karras and D. Solitar, Combinatorial Group Theory, Dover, New York, 1976.

S. J. Pride, Identities among relations of groups presentations, in Group theory from geometrical viewpoint – Trieste 1990, World Scientific Publishing Co. Pte. Ltd., Singapore, (1991) 687 – 717.

A. J. Sieradski, Combinatorial isomorphisma and combinatorial homotopy equivalences, J. Pure App. Algebra 7 (1976), 59 – 95

Yanita & A. G. Ahmad. 2009. Computing Generators of Second Homotopy Module Using Tietze Transformation Methods. Makalah yang dipresentasikan pada International Conference on Mathematics, Statistics and Their Applications, Bukittinggi, 9 – 11 Juni.




DOI: https://doi.org/10.29313/jmtm.v9i1.3477

Refbacks

  • There are currently no refbacks.


Copyright (c) 2018 Matematika

ISSN : 1412-5056 | E-ISSN 2598-8980  

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. 

Indexed by: