Надіслати цю статтю p-Groups with cyclic subgroup of index p and local nearrings
Анотація
p-Групи з циклічною підгрупою індексу p та локальні майже-кільця
Досліджено p-групи з циклічною підгрупою індексу p як адитивні групи та мультиплікативні групи локальних майже-кілець. Крім того, наведено класифікацію таких майже-кілець.
Зразок для цитування: M. Yu. Raievska, “p-Groups with cyclic subgroup of index p and local nearrings,” Прикл. проблеми механіки і математики, Вип. 22, 117–122 (2024), https://doi.org/10.15407/apmm2024.22.117-122
Ключові слова
Посилання
E. Aichinger, F. Binder, J. Ecker, P. Mayr, Ch. Nöbauer, SONATA – System of Nearrings and their Applications, Version 2.9.6 (2022), https://gap-packages.github.io/sonata/
B. Amberg, P. Hubert, Ya. Sysak, “Local nearrings with dihedral multiplicative group,” J. Algebra, 273, No. 2, 700–717 (2004), https://doi.org/10.1016/j.jalgebra.2003.10.007
T. H. H. Boykett, C. Nobauer, “A class of groups which cannot be the additive groups of near-rings with identity,” in: Contributions to General Algebra 10: Proc. of the Klagenfurt Conf. (May 29–June 1, 1997), Heyn, Klagenfurt (1998), pp. 89–99.
J. R. Clay, “Research in near-ring theory using a digital computer,” BIT Numerical Mathematics, 10, 249–265 (1970), https://doi.org/10.1007/BF01934196
J. R. Clay, J. J. Malone Jr., “The near-rings with identities on certain finite groups,” Math. Scand., 19, 146–150 (1966), https://doi.org/10.7146/math.scand.a-10803
J. R. Clay, C. J. Maxson, “The near-rings with identities on generalized quaternion groups,” Ist. Lombardo Accad. Sci. Lett. Rend. A, 104, P. 525–530 (1970).
S. Feigelstock, “Additive groups of local near-rings,” Commun. Algebra, 34, No. 2, 743–747 (2006), https://doi.org/10.1080/00927870500388042
GAP – Groups, Algorithms, Programming, Version 4.13.0 (2024), https://www.gap-system.org
A. Gorodnik, “Local near-rings with commutative groups of units,” Houston J. Math., 25, No.2, 223–234 (1999).
M. Hall Jr., The Theory of Groups, The Macmillan Company, New York (1959).
M. J. Johnson, “Near-rings with identities on dihedral groups,” Proc. Edinb. Math. Soc., 18, No. 3, 219–228 (1973), https://doi.org/10.1017/S0013091500009950
R. R. Laxton, R. Lockhart, “The near-rings hosted by a class of groups,” Procceedings of the Edinburgh Mathematical Society, 23, No. 1, 69–86 (1980), https://doi.org/10.1017/S001309150000362X
C. J. Maxson, “On local near-rings,” Math. Z., 106, No. 3, 197–205 (1968), https://doi.org/10.1007/BF01110133
C. J. Maxson, “Local near-rings of cardinality p2,” Canad. Math. Bull., 11, No. 4, P. 555–561 (1968), https://doi.org/10.4153/CMB-1968-066-2
C. J. Maxson, “On the construction of finite local near-rings (I): on non-cyclic abelian p-groups,” Q. J. Math., 21, No. 4, 449–457 (1970), https://doi.org/10.1093/qmath/21.4.449
C. J. Maxson, “On the construction of finite local near-rings (II): on non-abelian p-groups,” Q. J. Math., 22, No. 1, 65–72 (1971), https://doi.org/10.1093/qmath/22.1.65
J. D. P. Meldrum, Near-rings and their links with groups, London: Pitman Publ. (1985).
G. Pilz, Near-rings. The theory and its applications, North Holland, Amsterdam, 1977.
I. Yu. Raievska, M. Yu. Raievska, “Local nearrings with restrictions on the multiplicative groups and the subgroups of non-invertible elements,” Nauk. czasopys Nats. Pedag. Univ. im. Drahomanova, Ser. 1. Fiz.-Mat. Nauky, No. 14, 134–145 (2013) (in Ukrainian).
I. Yu. Raievska, M. Yu. Raievska, “Finite nearrings with identity on Miller–Moreno groups,” Mat. Stud., 42, No. 1, P. 15–20 (2014), https://doi.org/10.30970/ms.42.1.15-20
I. Yu. Raievska, M. Yu. Raievska, “Finite local nearrings,” Mohyla Mathematical Journal, 1, P. 38–48 (2018) (in Ukrainian), https://doi.org/10.18523/2617-7080i2018p38-48
I. Yu. Raievska, M. Yu. Raievska, Ya. P. Sysak, “Finite local nearrings with split metacyclic additive group,” Algebra Discrete Math., 22, No. 1, 129–152 (2016).
I. Raievska, M. Raievska, Y. Sysak, LocalNR. Package of local nearrings. Version 1.0.4 (2024), GAP package, https://gap-packages.github.io/LocalNR
I. Yu. Raievska, Ya. P. Sysak, “Finite local nearrings on metacyclic Miller–Moreno groups,” Algebra Discrete Math., 13, No. 1, P. 111–127 (2012).
M. Yu. Raievska, Ya. P. Sysak, “On local near-rings with Miller–Moreno multiplicative group,” Ukr. Mat. Zh., 64, No. 6, 811–818 (2012) (in Ukrainian); English translation: Ukr. Math. J., 64, No. 6, 930–937 (2012), https://doi.org/10.1007/s11253-012-0688-z
Ya. P. Sysak, S. Di Termini, “Local nearrings with generalized quaternion multiplicative group,” Ric. Mat., 56, 61–72 (2007), https://doi.org/10.1007/s11587-007-0005-6
Посилання
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