Atlas: Enumeration of Induced Cat1-groups of order 1-10. by Murat Alp

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International Conference on Applicable General Topology
August 12-18, 2001
Hacettepe University
Ankara, Turkey

Organizers
L. M. Brown (Ankara), G. Brümmer (Cape Town), M. Diker (Ankara), M. Henriksen (Claremont), R. D. Kopperman (New York), G. M. Reed (Oxford), I. L. Reilly (Auckland), S. Salbany (Pretoria), D. Spreen (Siegen)

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Enumeration of Induced Cat1-groups of order 1-10.
by
Murat Alp

In [3] we enumerated cat¹-groups of low order and we also enumerated Whitehead perm group of low order in [1]. Using the idea of these papers, we enumerated induced cat¹-groups of order 1 - 10 and we also describe a package of functions for computing crossed modules, their morphisms and derivations; Cat¹-groups, their morphisms and sections; Induced crossed modules and Induced Cat¹-groups and their morphisms in [4], written using the group theory programming language [10] (www-gap.dcs.st-andrews.ac.uk/~ gap/).

References [1] Alp, M., Enumeration of Whitehead Perm Groups of low order, International Journal of Algebra and Computation, To appear.

Alp, M., Left Adjoint of Pullback cat¹-groups, Turkish Journal of Mathematics, Vol. 23, No. 2, 1999, 243-249.

[3] Alp, M. and Wensley, C. D., Enumeration of Cat¹-groups of low order, International Journal of Algebra and Computation, Vol. 10, No: 4, 2000, 407-424.

[4] Alp, M. and Wensley, C. D., XMOD, Crossed modules and cat1-groups in GAP, version 1.3 Manual for the XMOD share package, Chapter 73, 1997, 1357- 1422.

[5] Brown, R., Triadic Van Kampen theorems and Hurewicz theorems, Contemporary Mathematics, Vol. 96, 1989, 39-57.

[6] Brown, R. and Wensley, C.D., On finite induced crossed modules, and the homotopy 2-type of mapping cones, Theory and Applications of Categories, 1 (3), 1995, 54-71.

[7] Brown, R. and Higgins, P. J., On the connection between the second relative homotopy group some related space, Proc. London. Math. Soc., 36, 1978, 193-212.

[8] Brown, R. and Loday, J. L., Homotopical excision, and Hurewicz theorems, for n-cubes of spaces, Proc. London Math. Soc., (3) 54, 1987, 176-192.

[9] Loday, J. L., Spaces with finitely many non-trivial homotopy groups, J.App.Algebra, 24, 1982, 179-202.

[10] Schönert, M. et al, GAP: Groups, Algorithms, and Programming, Lehrstuhl D für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany, third edition, 1993.

Date received: July 4, 2001