Finite nearrings with identity on Miller-Moreno groups

I. Yu. Raievska; M. Yu. Raievska

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2. Meldrum J.D.P. Near-rings and their links with groups. – London: Pitman Publishing Limited, 1985. – 273 p.

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4. Ferrero C.C., Ferrero G. Nearrings. Some developments linked to semigroups and groups. – Kluwer Academic Publishers, Dordrecht, 2002. – 609 p.

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7. Ligh S. Near rings with identities on certain groups// Monatsh. Math. – 1971. – V.75. – P. 38–43.

8. Krimmel J.E. A condition on near-rings with identity// Monatsh. Math. – 1973. – V.77. – P. 52–54.

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13. Redei L. Das “schiefe Produkt” in der Gruppentheorie mit Anwendung auf die endlichen nichtkommutativen Gruppen mit lauter kommutativen echten Untergruppen und die Ordnungszahlen, zu denen nur kommutative Gruppen gehoren// Comment. Math. Helv. – 1947. – V.20. – P. 225–264.

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15. Raievska I.Yu., Raievska M.Yu., Sysak Ya.P. Local nearrings on nonmetacyclic Miller-Moreno groups// Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics. – 2012. – V.3. – P. 39–46. (in Ukrainian)

16. Raievska I.Yu., Sysak Ya.P. Finite local nearrings on metacyclic Miller-Moreno p-groups// Algebra and Discrete Mathematics. – 2012. – V.13, №1. – P. 111–127.

	Finite nearrings with identity on Miller-Moreno groups
Author	I. Yu. Raievska, M. Yu. Raievska raemarina@rambler.ru Institute of Mathematics of NAS of Ukraine
Abstract	In this paper all possible types of Miller-Moreno groups which can be the additive groups of nearrings with identity are described.
Keywords	nearring with identity; additive group; Miller-Moreno group
Reference	1. Pilz G. Near-rings. The theory and its applications. – North Holland, Amsterdam, 1977. 2. Meldrum J.D.P. Near-rings and their links with groups. – London: Pitman Publishing Limited, 1985. – 273 p. 3. Clay J.R. Nearrings. Geneses and applications. – New York: Clarendon Press, Oxford University Press, 1992. 4. Ferrero C.C., Ferrero G. Nearrings. Some developments linked to semigroups and groups. – Kluwer Academic Publishers, Dordrecht, 2002. – 609 p. 5. Clay J.R., Malone Jr. The near-rings with identities on certain finite groups// Math. Scand. – 1966. – V.19. – P. 146–150. 6. Clay J.R., Doi D. Near-rings with identity on alternating groups// Math. Scand. – 1968. – V.23. – P. 54–56. 7. Ligh S. Near rings with identities on certain groups// Monatsh. Math. – 1971. – V.75. – P. 38–43. 8. Krimmel J.E. A condition on near-rings with identity// Monatsh. Math. – 1973. – V.77. – P. 52–54. 9. Clay J.R. Research in near-ring theory using a digital computer// BIT. – 1970. – V.10. – P. 249–265. 10. Clay J.R., Maxson C.J. The near-rings with identities on generalized quaternion groups// Ist. Lombardo Accad. Sci. Lett. Rend. A. – 1970. – V.104. – P. 525–530. 11. Johnson M.J. Near-rings with identities on dihedral groups// Proceedings of the Edinburgh Mathematical Society. – 1973. – V.18. – P. 219–228. 12. Boykett T.H.H., Nobauer C. A class of groups which cannot be the additive groups of near-rings with identity// Contributions to general algebra. Klagenfurt: Heyn. – 1998. – V.10. – P. 89–99. 13. Redei L. Das “schiefe Produkt” in der Gruppentheorie mit Anwendung auf die endlichen nichtkommutativen Gruppen mit lauter kommutativen echten Untergruppen und die Ordnungszahlen, zu denen nur kommutative Gruppen gehoren// Comment. Math. Helv. – 1947. – V.20. – P. 225–264. 14. Aichinger E., Binder F., Ecker J., Mayr P., Nobauer C. SONATA – system of near-rings and their applications, GAP package, Version 2.6; 2012. (http:// www.algebra.uni-linz.ac.at/Sonata/) 15. Raievska I.Yu., Raievska M.Yu., Sysak Ya.P. Local nearrings on nonmetacyclic Miller-Moreno groups// Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics. – 2012. – V.3. – P. 39–46. (in Ukrainian) 16. Raievska I.Yu., Sysak Ya.P. Finite local nearrings on metacyclic Miller-Moreno p-groups// Algebra and Discrete Mathematics. – 2012. – V.13, №1. – P. 111–127.
Pages	15-20
Volume	42
Issue	1
Year	2014
Journal	Matematychni Studii
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Table of content of issue	html