Title | On the groups, whose all subgroups with infinite special rank are transitively normal |
Publication Type | Journal Article |
Year of Publication | 2017 |
Authors | Semko, NN, Velichko, TV |
Abbreviated Key Title | Dopov. Nac. akad. nauk Ukr. |
DOI | 10.15407/dopovidi2017.08.017 |
Issue | 8 |
Section | Mathematics |
Pagination | 17-19 |
Date Published | 8/2017 |
Language | Ukrainian |
Abstract | The periodic soluble groups, whose subgroups with infinite special rank are transitively normal, and the struc ture of a periodic radical group, whose subgroups with infinite special rank are transitively normal, are described. |
Keywords | finite special rank, locally nilpotent radical, locally nilpotent residual, periodic group, soluble group, transitively normal subgroups |
References:
- Maltsev, A. I. (1948). On groups of finite rank. Mat. Sbornik, 22, pp. 351-352 (in Russian).
- Dixon, M. R., Kurdachenko, L. A. & Subbotin, I. Ya. (2007). On various rank conditions in infinite groups. Algebra Discrete Math., 4, pp. 23-44.
- Dixon, M. R. (2008). Certain rank conditions on groups. Noti di Matematica, 2, pp. 151-175.
- Dixon, M. R., Kurdachenko, L. A., Pypka, A. A. & Subbotin, I. Ya. (2016). Groups satisfying certain rank conditions. Algebra Discrete Math., 4, pp. 23-44.
- Dixon, M. R., Evans, M. J. & Smith, H. (1997). Locally (soluble-by-finite) groups with all proper insoluble subgroups of finite rank. Arch. Math. (Basel), 68, pp. 100-109. https://doi.org/10.1007/s000130050037
- Kurdachenko, L. A. & Subbotin, I. Ya. (2006). Transitivity of normality and pronormal subgroups. In Combinatorial group theory, discrete groups, and number theory. Contemporary Mathematics, Vol. 421 (pp. 201-212). Providence, RI: Amer. Math. Soc. https://doi.org/10.1090/conm/421/08038
- Mysovskikh, V. I. (1999). Subnormalizers and properties of embedding of subgroups in finite groups. Zap. Nauchn. Sem. POMI, 265, pp. 258-280 (in Russian).
- Kirichenko, V. V., Kurdachenko, L. A. & Subbotin, I. Ya. (2011). Some related to pronormality subgroup families and the properties of a group. Algebra Discrete Math., 1, pp. 75-108.
- Baer, R. (1933). Situation der Untergruppen und Struktur der Gruppe. S.-B. Heidelberg Akad., 2, pp. 12-17.