Abstract
After a historical introduction this report announces in detail seventeen theorems about endomorphism nearrings on finite groups for various groups and classes of groups, mainly without proofs or only sketching some proofs, but indicating instead which theorems with their full proofs we plan to publish together in one paper and what headings these papers will have.
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References
J. L. Alperin and D. Gorenstein. The multiplicators of certain simple groups. Proc. Amer. Math. Soc. 17 (1966), 515–519.
J. R. Clay. Nearrings: Geneses and Applications. Oxford University Press. Oxford, New York, Tokyo 1992.
Y. Fong. The endomorphism near-rings of the symmetric groups. Dissertation, Ph. D. University of Edinburgh, U. K. 1979.
Y. Fong and J. D. P. Meldrum. The endomorphism near-rings of the symmetric groups of degree at least five. J. Austral. Math. Soc. 30A (1980), 37–49.
Y. Fong and J. D. P. Meldrum. The endomorphism near-ring of the symmetric group of degree four. Tamkang J. Math. 12 (1981), 193–203.
A. Fröhlich. The near-ring generated by the inner automorphisms of a finite simple group. J. London Math. Soc. 33 (1958), 95–107.
D. Gorenstein. Finite simple groups: An introduction to their classification. Plenum Press. New York 1982.
R. L. Griess. Schur multipliers of the known finite simple groups II. Proc. Amer. Math. Soc 37 (1980), 279–282.
B. Huppert. Endliche Gruppen I. Springer-Verlag. Berlin, Heidelberg, New York 1967.
C. G. Lyons and J. J. Malone. Endomorphism near-rings. Proc. Edinburgh Math. Soc. 17 (1970), 71–78.
C. G. Lyons and J. J. Malone. Finite dihedral groups and d. g. near-rings I. Compo-sitio Mathematica 24 (1972), 305–312.
C. G. Lyons and J. J. Malone. Finite dihedral groups and d. g, near-rings II. Com-positio Mathematica 26 (1973), 249–259.
C. G. Lyons and G. Mason. Endomorphism near-rings of dicyclic and generalised dihedral groups, Proc. Royal Irish Acad. 91A (1991), 99–111.
C. G. Lyons and J. D, P. Meldrum. Reduction theorems for endomorphism near-rings. Monatsh. Math. 89 (1980), 301–313.
J. J. Malone. Generalized quaternion groups and distributively generated near-rings. Proc. Edinburgh Math. Soc. 18 (1973), 235–238.
J. J. Malone and G. Mason. ZS-metacyclic groups and their endomorphism near-rings. To appear in Monatsh. Math.
J. D. P. Meldrum. On the structure of morphism near-rings. Proc. Royal Soc. Edinburgh 81A (1978), 287–298.
J. D. P. Meldrum. The endomorphism near-rings of finite general linear groups. Proc. Royal Irish Acad. 79A (1979), 87–96.
J. D. P. Meldrum. Near-rings and their links with groups. Research Notes in Mathematics 134. Pitman Adv. Publ. Program. Boston, London 1985.
G. Pilz. Near-rings. North-Holland/American Elsevier. Amsterdam 1977. Revised Edition 1983.
J. J. Rotman. The theory of groups. Allyn and Bacon. Boston 1973.
G. Saad, S. A. Syskin and M. J. Thomsen. The coincidence of some nearrings defined by symmetric groups. Intern, Conf. on Algebra. Book of Abstracts, p.432-433. Krasnoyarsk (Russia) 1993.
G. Saad, S. A. Syskin and M. J. Thomsen. The general linear group GL(2,3) and related nearrings. Intern. Conf. on Algebra. Book of Abstracts, p.433-434. Krasnoyarsk (Russia) 1993.
G. Saad, S. A. Syskin and M. J. Thomsen. On endomorphism nearrings of symmetric-groups. To appear in Results in Mathematics 26 (1994).
G. Saad, S. A. Syskin and M. J. Thomsen. Some linear groups and their endomorphism nearrings. To appear.
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© 1995 Springer Science+Business Media Dordrecht
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Saad, G., Thomsen, M.J., Syskin, S.A. (1995). Endomorphism Nearrings on Finite Groups, a Report. In: Fong, Y., Bell, H.E., Ke, WF., Mason, G., Pilz, G. (eds) Near-Rings and Near-Fields. Mathematics and Its Applications, vol 336. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0359-6_25
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DOI: https://doi.org/10.1007/978-94-011-0359-6_25
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