On the numerical characteristics of the factors of the central series and their relationships in some algebraic structures
Problemy fiziki, matematiki i tehniki, no. 4 (2017), pp. 71-75.

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

The relationships between some numerical characteristics of the members and factors of the upper and lower central series in groups and Lie algebras are investigated.
Keywords: Schur’s theorem, Baer’s theorem, special rank, section p-rank, upper (lower) central series of Lie algebra.
@article{PFMT_2017_4_a12,
     author = {A. A. Pypka},
     title = {On the numerical characteristics of the factors of the central series and their relationships in some algebraic structures},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {71--75},
     publisher = {mathdoc},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2017_4_a12/}
}
TY  - JOUR
AU  - A. A. Pypka
TI  - On the numerical characteristics of the factors of the central series and their relationships in some algebraic structures
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2017
SP  - 71
EP  - 75
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2017_4_a12/
LA  - ru
ID  - PFMT_2017_4_a12
ER  - 
%0 Journal Article
%A A. A. Pypka
%T On the numerical characteristics of the factors of the central series and their relationships in some algebraic structures
%J Problemy fiziki, matematiki i tehniki
%D 2017
%P 71-75
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2017_4_a12/
%G ru
%F PFMT_2017_4_a12
A. A. Pypka. On the numerical characteristics of the factors of the central series and their relationships in some algebraic structures. Problemy fiziki, matematiki i tehniki, no. 4 (2017), pp. 71-75. http://geodesic.mathdoc.fr/item/PFMT_2017_4_a12/

[1] B.H. Neumann, “Groups with finite classes of conjugate elements”, Proc. London Math. Soc., 1 (1951), 178–187 | DOI | MR | Zbl

[2] L.A. Kurdachenko, I.Ya. Subbotin, “A brief history of an important classical theorem”, Advances in Group Theory and Applications, 2 (2016), 121–124 | MR | Zbl

[3] J. Wiegold, “Multiplicators and groups with finite central factor-groups”, Math. Z., 89:4 (1965), 345–347 | DOI | MR | Zbl

[4] A.A. Pypka, D.Yu. Storozhenko, “On Wiegold's function”, 11th International Algebraic Conference in Ukraine dedicated to the 75th anniversary of V.V. Kirichenko (July 3–7, 2017), 110 | MR

[5] R. Baer, “Endlichkeitskriterien fur Kommutatorgruppen”, Math. Ann., 124 (1952), 161–177 | DOI | MR | Zbl

[6] L.A. Kurdachenko, I.Ya. Subbotin, “On some properties of the upper and lower central series”, Southeast Asian Bull. Math., 37:4 (2013), 547–554 | MR | Zbl

[7] M.R. Dixon, L.A. Kurdachenko, A.A. Pypka, “The theorems of Schur and Baer: a survey”, International Journal of Group Theory, 4:1 (2015), 21–32 | MR

[8] L.A. Kurdachenko, I.Ya. Subbotin, “On the relationships between the factors of upper and lower central series in groups and other algebraic structures”, Noti di Math., 36:1 (2016), 35–50 | MR

[9] L.A. Kurdachenko, P. Shumyatsky, “The ranks of central factor and commutator groups”, Math. Proc. Cambridge Phil. Soc., 154 (2013), 63–69 | DOI | MR | Zbl

[10] L.A. Kurdachenko, J. Otal, “The rank of the factorgroup modulo the hypercenter and the rank of the some hypocenter of a group”, Central European Journal of Mathematics, 11 (2013), 1732–1741 | MR | Zbl

[11] A. Ballester-Bolinches, S. Camp-Mora, L.A. Kurdachenko, J. Otal, “Extension of a Schur theorem to groups with a central factor with a bounded section rank”, Journal Algebra, 393 (2013), 1–15 | DOI | MR | Zbl

[12] L.A. Kurdachenko, N.N. Semko, A.A. Pypka, “On some relationships between the upper and lower central series in finite groups”, Proceedings of the F. Scorina Gomel State University, 2014, no. 3(84), 66–71 | MR

[13] I.N. Stewart, “Verbal and marginal properties of non-associative algebras”, Proc. Lond. Math. Soc., III Ser., 28 (1974), 129–140 | DOI | MR | Zbl

[14] M.R. Vaughan-Lee, “Metabelian BFC $p$-groups”, J. Lond. Math. Soc., II Ser., 5 (1972), 673–680 | DOI | MR | Zbl

[15] L.A. Kurdachenko, J. Otal, A.A. Pypka, “Relationships between factors of canonical central series of Leibniz algebras”, Eur. J. Math., 2 (2016), 565–577 | DOI | MR | Zbl