Abstract
A Z-constrained N-group is one without central minimal factors. Z-constrained tame nearrings with DCCR are defined differently but in accordance with this definition. A 3-tame nearing N has a unique maximal locally N-nilpotent right N-subgroup L(N). This right N-subgroup is an ideal. It is shown that if, for a compatible nearing N with DCCR, N/L(N) is Z-constrained, then all Fitting factors of faithful compatible N-groups are N-isomorphic. A number of other formulations of this theorem are possible. It is a big result that requires investigation into many other areas. One important concept, on which the proof rests, is that of realisations.
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References
E. Aichinger, On Near-ring Idempotents and Polynomials on Direct Products of Ω-groups, Proc. Edin. Math. Soc. 44 (2001), 379–388.
J. D. P. Meldrum, Nearrings and their Links with Groups, Pitman Publishing, Lon. (1985).
G. L. Peterson, On an Isomorphism Problem for Endomorphism Near-rings, Proc. Amer. Math. Soc. 126 (1998), no.7. 1897–1900.
G. Pilz, Nearrings, North-Holland Pub (1983). Amsterdam.
S. D. Scott, Central Factors of 2-tame N-groups, 10 page manuscript (1996).
S. D. Scott, Compatible Nearrings, 146 page unpublished book (2000).
S. D. Scott, Compatible Z-constrained N-groups, 4 page manuscript (1997).
S. D. Scott, Idempotents in Near-rings with Minimal Condition, J. Lon. Math. Soc. (2) 6 (1973), 464–466.
S. D. Scott, Linear Ω-Groups, Polynomial Maps. Contr. Gen. Alg. 8 (1991), 239–293.
S. D. Scott, Minimal Ideals of Near-rings with Minimal Condition, J. Lon. Math. Soc. (2) 8 (1974), 8–12.
S. D. Scott, Near-rings and near-ring modules, Doct. diss. (Austr. Nat. Uni. 1970).
S. D. Scott, N-solubility and N-nilpotency in Tame N-groups, Alg. Col. 5:4 (1998), 425–448.
S. D. Scott, On the Finiteness and Uniqueness of Certain 2-tame N-groups, Proc. Edin. Math. Soc. 38 (1995), 193–205.
S. D. Scott, On the Structure of Certain 2-Tame Near-rings, Klu. Acad. Pub. (1995) (Netherlands), Near-rings and Near-fields, 239–256.
S. D. Scott, Tame Fusion, Alg. Col. 10:4 (2003), 543–566.
S. D. Scott, Tame Near-rings and N-Groups. Proc. Edin. Math. Soc. 23 (1980), 275–296.
S. D. Scott, Tameness and the Right Ideal Q(N). Alg. Col. 6:4 (1999), 413–438.
S. D. Scott, The Structure of Ω-Groups. Klu. Acad. Pub (1997) (Netherlands), Nearrings, Nearfields and K-loops, 47–137.
S. D. Scott, The Uniqueness of Certain Compatible N-groups, 29 page manuscript (1997).
S. D. Scott, Topology and Primary N-groups, Klu. Acad. Pub. (2001) (Netherlands), Near-rings and Near-fields, 151–197.
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Scott, S.D. (2005). The Z-Constrained Conjecture. In: Kiechle, H., Kreuzer, A., Thomsen, M.J. (eds) Nearrings and Nearfields. Springer, Dordrecht. https://doi.org/10.1007/1-4020-3391-5_5
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DOI: https://doi.org/10.1007/1-4020-3391-5_5
Publisher Name: Springer, Dordrecht
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