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On solvable groups and rings definable in o-minimal structures

from RESEARCH ARTICLES

Published online by Cambridge University Press:  30 March 2017

Jan Van Eijck
Affiliation:
Centre for Mathematics and Computer Science, Amsterdam
Vincent Van Oostrom
Affiliation:
Universiteit Utrecht, The Netherlands
Albert Visser
Affiliation:
Universiteit Utrecht, The Netherlands
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Publisher: Cambridge University Press
Print publication year: 2004

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References

[1] M., Edmundo, Solvable groups definable in o-minimal structures, Preprint (submitted), 2000.
[2] M., Edmundo, Structure theorems for o-minimal expansions of groups, Annals of Pure and Applied Logic, vol. 102 (2000), pp. 159-181.Google Scholar
[3] S., Eilenberg and S., MacLane, Cohomology theory in abstract groups I, Annals of Mathematics, vol. 48 (1947), pp. 51-78.Google Scholar
[4] S., Eilenberg and S., MacLane, Cohomology theory in abstract groups II, Annals of Mathematics, vol. 48 (1947), pp. 326-341.Google Scholar
[5] D., Macpherson, A., Mosley, and K., Tent, Permutation groups in o-minimal structures, Preprint, 1999.
[6] C., Miller, A growth dichotomy for o-minimal expansions of ordered fields, Preprint, 1996.
[7] C., Miller and S., Starchenko, A growth dichotomy for o-minimal expansions of ordered groups, Logic colloquium 93 (W., Hodges et al., editors), Oxford University Press, 1994, Preprint 1995.
[8] A., Nesin, Solvable groups of finite morley rank, Journal of Algebra, vol. 121 (1989), pp. 26- 39.Google Scholar
[9] O., Otero, Y., Peterzil, and A., Pillay, Ongroups and rings definable in o-minimal expansions of real closed fields, The Bulletin of the London Mathematical Society, vol. 28 (1996), pp. 7-14.Google Scholar
[10] Y., Peterzil, A., Pillay, and S., Starchenko, Linear groups definable in o-minimal structures, Preprint, 1999.
[11] Y., Peterzil, A., Pillay, and S., Starchenko, Definably simple groups in o-minimal structures, Transactions of the American Mathematical Society, vol. 352 (2000), no. 10, pp. 4397-4419.Google Scholar
[12] Y., Peterzil, A., Pillay, and S., Starchenko, Simple algebraic groups over real closed fields, Transactions of the American Mathematical Society, vol. 352 (2000), no. 10, pp. 4421-4450.Google Scholar
[13] Y., Peterzil and S., Starchenko, A trichotomy theorem for o-minimal structures, Proceedings of the London Mathematical Society, vol. 77 (1998), pp. 481-523.Google Scholar
[14] Y., Peterzil and S., Starchenko, Definable homomorphisms of abelian groups in o-minimal structures, Annals of Pure and Applied Logic, vol. 101 (1999), no. 1, pp. 1-27.Google Scholar
[15] Y., Peterzil and C., Steinhorn, Definable compacteness and definable subgroups of ominimal groups, The Journal of the London Mathematical Society, vol. 59 (1999), no. 2, pp. 769- 786.Google Scholar
[16] A., Pillay, On groups and fields definable in o-minimal structures, Journal of Pure and Applied Algebra, vol. 53 (1988), pp. 239-255.Google Scholar
[17] V., Razenj, One-dimensional groups over an o-minimal structure, Journal of Pure and Applied Algebra, vol. 53 (1991), pp. 269-277.Google Scholar
[18] A., Strzebonski, Euler characteristic in semialgebraic and other o-minimal groups, Journal of Pure and Applied Algebra, vol. 96 (1994), pp. 173-201.Google Scholar
[19] L., van den Dries, Tame topology and o-minimal structures, Cambridge University Press, 1998.

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