A note on analogue of Koethe conjecture in group theory

W. Holubowski

doi:10.30970/ms.65.2.217-219

W. Holubowski Department of Mathematics Faculty of Applied Mathematics Silesian University of Technology Gliwice, Poland

DOI: https://doi.org/10.30970/ms.65.2.217-219

Keywords: p−subgroups, complex product of groups, torsion elements

Abstract

We give a negative answer to a question in group theory proposed by Vitalyi Sushchanskyy which is an analogue of Koethe conjecture in ring theory.

Author Biography

W. Holubowski, Department of Mathematics Faculty of Applied Mathematics Silesian University of Technology Gliwice, Poland

Department of Mathematics
Faculty of Applied Mathematics
Silesian University of Technology
Gliwice, Poland

References

T. Banakh, A. Ravsky, On Unconditionally Convergent Series in Topological Rings, Carpathian Math. Publ. 14 (1) (2022), 266–288. https://doi.org/10.15330/cmp.14.1.266-288

A. Chigogidze, Inverse Spectra, North Holland, Amsterdam, 1996.

M.A. Chebotar, P.-H. Lee, E.R. Puczy lowski, On Some Questions Related to Koethe’s Nil Ideal Problem, Proc. Edinb. Math. Soc. (2) 59 (1) (2016), 57–64. https://doi.org/10.1017/S0013091514000273

W. Ho lubowski, Free Subgroups of the Group of Infinite Unitriangular Matrices, Internat. J. Algebra Comput. 13 (1) (2003), 81–86. https://doi.org/10.1142/S0218196703001341

J. Krempa, Logical connections between some open problems concerning nil rings, Fund. Math. 76 (1972), 121–130. https://matwbn.icm.edu.pl/ksiazki/fm/fm76/fm76112.pdf

G. Kothe, Die Struktur der Ringe, Deren Restklassenring Nach dem Radikal Vollst¨andig Reduzibel Ist, Math. Z. 32 (1930), 161–186. https://doi.org/10.1007/BF01194626

L.H. Rowen, Koethe’s Conjecture, Israel Mathematical Conference Proceedings, V.1, 193–202 (Weizmann, Jerusalem, 1989).

A. Smoktunowicz, On Some Results Related to Koethe’s Conjecture, Serdica Math. J. 27 (2) (2001), 159–170. http://hdl.handle.net/10525/474