The graph of generating sets of an abelian group

• Autorzy: Persi Diaconis , Ronald Graham
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1999
• Tom: 80
• Numer: 1
• Strony: 31-38

Daty

wydano

1999

otrzymano

1997-12-19

poprawiono

1998-04-15

Twórcy

autor

Persi Diaconis

• Departments of Mathematics and Statistics, Stanford University, Stanford, California 94305 U.S.A.

autor

Ronald Graham

• AT&T Labs, Florham Park, New Jersey 07932, U.S.A.

Bibliografia

• [1] Celler, F., Leedham-Green, C., Murray, S., Wiemeyer, A. and O'Brien, E., Generating random elements of a finite group, Comm. Algebra 23 (1995), 4831-4948.
• [2] Chung, F. R. K., Spectral Graph Theory, CBMS Regional Conf. Ser. in Math. 92, Amer. Math. Soc., Providence, 1997.
• [3] Chung, F. and Graham, R., Random walks on generating sets for finite groups, Electron. J. Combin. 2 (1997), no. R7.
• [4] Chung, Stratified random walks on an $n$-cube, Random Structures Algorithms (1997), to appear.
• [5] Dennis, R. K. and Geller, S. C., $K_i$ of upper triangular matrix rings, Proc. Amer. Math. Soc. 56 (1976), 73-78.
• [6] Diaconis, P., Group Representations in Probability and Statistics, IMS Lecture Notes--Monograph Ser. 11, Inst. Math. Statist., Hayward, CA, 1988.
• [7] Diaconis, P. and Saloff-Coste, L., Random walks on finite groups: A survey of analytic techniques, in: Probability Measures on Groups and Related Structures, XI, H. Heyer (ed.), World Scientific, River Edge, NJ, 1995, 44-75.
• [8] Diaconis, Walks on generating sets of abelian groups, Probab. Theory Related Fields 105 (1996), 393-421.
• [9] Diaconis, Walks on generating sets of groups, Technical Report, Dept. of Statistics, Stanford Univ., 1996.
• [10] Dunwoody, M., On $T$-systems of groups, J. Austral. Math. Soc. 3 (1963), 172-179.
• [11] Hall, P., The Eulerian functions of a group, Quart. J. Math. 7 (1936), 134-151.
• [12] Holt, D. and Rees, S., An implementation of the Neumann-Praeger algorithm for the recognition of special linear groups, J. Experiment. Math. 1 (1992), 237-292.
• [13] Laffrety, J. and Rockmore, D., Personal communication, 1997.
• [14] Neumann, B., On a question of Gaschütz, Arch. Math. (Basel) 7 (1956), 87-90.
• [15] Neumann, B. H. and Neumann, H., Zwei Klassen charakteristischer Untergruppen und ihre Faktorgruppen, Math. Nachr. 4 (1951), 106-125.
• [16] Rosenberg, J., Algebraic $K$-Theory and its Applications, Grad. Texts in Math. 147, Springer, New York, 1994.
• [17] Schrijver, A., Theory of Linear and Integer Programming, Wiley, Chichester, 1986.