On the structure of groups whose non-abelian subgroups are serial

TitleOn the structure of groups whose non-abelian subgroups are serial
Publication TypeJournal Article
Year of Publication2016
AuthorsDixon, MR, Kurdachenko, LA, Semko, NN
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2016.07.022
Issue7
SectionMathematics
Pagination22-26
Date Published7/2016
LanguageUkrainian
Abstract

We obtain a detailed description of non locally nilpotent locally finite groups, whose non-abelian subgroups are serial, ascendant, or permutable.
Keywordsascendant subgroup, local finite group, permutable subgroup, serial subgroup
References: 
  1. Dedekind R. Math. Ann., 1897, 48: 548–561. https://doi.org/10.1007/BF01447922
  2. Lennox J. C., Stonehewer S. E. Subnormal subgroups of groups, Oxford: Clarendon Press, 1987.
  3. Casolo C. Note Mat., 2008, 28, suppl. 2: 1–149.
  4. Miller G. A., Moreno H. C. Trans. Amer. Math. Soc., 1903, 4: 389–404.
  5. Schmidt O.Yu. Mat. Sb., 1924, 31, No 3: 366–372 (in Russian).
  6. Ol'shanskij A.Yu. Geometry of defining relations in groups, Moscow: Nauka, 1989 (in Russian).
  7. Asar A. O. J. London Math., 2000, 61: 412–422. https://doi.org/10.1112/S0024610799008479
  8. Romalis G. M., Sesekin N. F. Matem. Zap. Ural. Univ., 1966, 5, No 3: 45–49 (in Russian).
  9. Kuzenny N. F., Semko N. N. Metahamiltonian groups and their generalizations, Kyiv: Math. Institute of the NAS of Ukraine, 1996 (in Ukrainian).
  10. Phillips R. E., Wilson J. S. J. Algebra, 1978, 51: 41–68. https://doi.org/10.1016/0021-8693(78)90134-5
  11. Bruno B., Phillips R. Math. Z., 1981, 176, No 2: 199–221. https://doi.org/10.1007/BF01261869
  12. Smith H. Quad. Mat., 2001, 8: Topics in infinite groups: 309–326.
  13. Smith H. Quad. Mat., 2001, 8: Topics in infinite groups: 297–308.
  14. Kurdachenko L. A., Atlihan S., Semko N. N. Central Eur. J. Math., 2014, 12, No 12: 1762–1771.
  15. de Falco M., de Giovanni F., Musella C., Schmidt R. Rend. Circ. Mat. Palermo (2), 2003, 52, No 1: 70–76.