Geodesic
Finite local nearrings with split metacyclic additive group
Algebra and discrete mathematics, Tome 22 (2016) no. 1, pp. 129-152.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper the split metacyclic groups which are the additive groups of finite local nearrings are classified.
Keywords: nearring with identity, local nearring, additive group, split metacyclic group. 
@article{ADM_2016_22_1_a8,
     author = {I. Yu. Raievska and M. Yu. Raievska and Ya. P. Sysak},
     title = {Finite local nearrings with split metacyclic additive group},
     journal = {Algebra and discrete mathematics},
     pages = {129--152},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2016_22_1_a8/}
}
TY  - JOUR
AU  - I. Yu. Raievska
AU  - M. Yu. Raievska
AU  - Ya. P. Sysak
TI  - Finite local nearrings with split metacyclic additive group
JO  - Algebra and discrete mathematics
PY  - 2016
SP  - 129
EP  - 152
VL  - 22
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2016_22_1_a8/
LA  - en
ID  - ADM_2016_22_1_a8
ER  - 
%0 Journal Article
%A I. Yu. Raievska
%A M. Yu. Raievska
%A Ya. P. Sysak
%T Finite local nearrings with split metacyclic additive group
%J Algebra and discrete mathematics
%D 2016
%P 129-152
%V 22
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2016_22_1_a8/
%G en
%F ADM_2016_22_1_a8
I. Yu. Raievska; M. Yu. Raievska; Ya. P. Sysak. Finite local nearrings with split metacyclic additive group. Algebra and discrete mathematics, Tome 22 (2016) no. 1, pp. 129-152. http://geodesic.mathdoc.fr/item/ADM_2016_22_1_a8/

[1] B. Amberg, P. Hubert, Ya. Sysak, “Local near-rings with dihedral multiplicative group”, J. Algebra, 273 (2004), 700–717 | DOI | MR | Zbl

[2] J. N. S. Bidwell, M. J. Curran, “The automorphism group of a split metacyclic $p$-group”, Arch. Math., 87 (2006), 488–497 | DOI | MR | Zbl

[3] J. R. Clay, “Research in near-ring theory using a digital computer”, BIT, 10 (1970), 249–265 | DOI | MR | Zbl

[4] M. J. Curran, “The automorphism group of a split metacyclic $2$-group”, Arch. Math., 89 (2007), 10–23 | DOI | MR | Zbl

[5] S. Feigelstock, “Additive Groups of Local Near-Rings”, Comm. Algebra, 34 (2006), 743–747 | DOI | MR | Zbl

[6] M. J. Johnson, “Near-rings with identities on dihedral groups”, Proc. Edinburgh Math. Soc. (2), 18 (1972/73), 219–228 | DOI | MR

[7] B. W. King, “Presentations of metacyclic groups”, Bul. Austral. Math. Soc., 8 (1973), 103–131 | DOI | MR | Zbl

[8] C. J. Maxson, “On local near-rings”, Math. Z., 106 (1968), 197–205 | DOI | MR | Zbl

[9] C. J. Maxson, “Local near-rings of cardinality $p^2$”, Canad. Math. Bull., 11:4 (1968) | MR

[10] C. J. Maxson, “On the construction of finite local near-rings (I): on non-cyclic abelian $p$-groups”, Quart. J. Math. Oxford (2), 21 (1970), 449–457 | DOI | MR | Zbl

[11] C. J. Maxson, “On the construction of finite local near-rings (II): on non-abelian $p$-groups”, Quart. J. Math. Oxford (2), 22 (1971), 65–72 | DOI | MR | Zbl

[12] J. D. P. Meldrum, Near-rings and their links with groups, Pitman research notes in mathematics, 134, 1985, 273 pp. | MR | Zbl

[13] G. Pilz, Near-rings. The theory and its applications, Second edition, North-Holland, Amsterdam, 1983, 470 pp. | MR | Zbl

[14] I. Yu. Raievska, M. Yu. Raievska, “Finite nearrings with identity on Miller–Moreno groups”, Mat. Stud., 42:1 (2014), 15–20 | MR | Zbl

[15] I. Yu. Raievska, Ya. P. Sysak, “Finite local nearrings on metacyclic Miller–Moreno $p$-groups”, Algebra and Discrete Math., 13:1 (2012), 111–127 | MR | Zbl