On the structure of groups whose non-abelian subgroups are serial
DOI:
https://doi.org/10.15407/dopovidi2016.07.022Keywords:
local finite group, serial subgroup, ascendant subgroup, permutable subgroupAbstract
We obtain a detailed description of non locally nilpotent locally finite groups, whose non-abelian subgroups are serial, ascendant, or permutable.
Downloads
References
Dedekind R. Math. Ann., 1897, 48: 548–561.
Lennox J. C., Stonehewer S. E. Subnormal subgroups of groups, Oxford: Clarendon Press, 1987.
Casolo C. Note Mat., 2008, 28, suppl. 2: 1–149.
Miller G. A., Moreno H. C. Trans. Amer. Math. Soc., 1903, 4: 389–404.
Schmidt O.Yu. Mat. Sb., 1924, 31, No 3: 366–372 (in Russian).
Ol’shanskij A.Yu. Geometry of defining relations in groups, Moscow: Nauka, 1989 (in Russian).
Asar A. O. J. London Math., 2000, 61: 412–422.
Romalis G. M., Sesekin N. F. Matem. Zap. Ural. Univ., 1966, 5, No 3: 45–49 (in Russian).
Kuzenny N. F., Semko N. N. Metahamiltonian groups and their generalizations, Kiev: Math. Institute of the NAS of Ukraine, 1996 (in Ukrainian).
Phillips R. E., Wilson J. S. J. Algebra, 1978, 51: 41–68.
Bruno B., Phillips R. Math. Z., 1981, 176, No 2: 199–221.
Smith H. Quad. Mat., 2001, 8: Topics in infinite groups: 309–326.
Smith H. Quad. Mat., 2001, 8: Topics in infinite groups: 297–308.
Kurdachenko L. A., Atlihan S., Semko N. N. Central Eur. J. Math., 2014, 12, No 12: 1762–1771.
de Falco M., de Giovanni F., Musella C., Schmidt R. Rend. Circ. Mat. Palermo (2), 2003, 52, No 1: 70–76.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Reports of the National Academy of Sciences of Ukraine
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
