Groups with the minimal condition on non-``abelian-by-finite'' subgroups |
|
| Author |
artemovych@franko.lviv.ua
Faculty of Mechanics and Mathematics,Ivan Franko National University of Lviv
|
| Abstract |
We characterize groups in which no non-trivial section is perfect without infinite properly descending series of non-``abelian-by-finite'' subgroups.
|
| Keywords |
group, non-perfect non-trivial section, infinite properly descending series of non-abelian-by-finite subgroups
|
| DOI |
doi:10.30970/ms.22.2.215-219
|
Reference |
1. V.V. Belyaev Locally finite groups with almost abelian proper subgroups, Siberian Math. Zh. 24 (1983), 11--17. (in Russian)
2. Bruno B. On groups with abelian-by-finite proper subgroups, Boll. Un. Mat. Ital. (6) 3-B (1984), 797--807. 3. Bruno B. Gruppi i cui sottogruppi propri contengono un sottogruppo nilpotente di indice finito, Bull. Un. Mat. Ital. (6) 3-D (1984), 179--188. 4. Bruno B. Special $q$-groups and ${\Bbb C}_{p^\infty}$-groups of automorphisms, Archiv Math. 48 (1987), 15--24. 5. Bruno B. and Phillips R.E. A note on groups with nilpotent-by-finite proper subgroups, Archiv Math. 65 (1995), 369--374. 6. Robinson D.J.S. Finiteness conditions and generalized soluble groups, Part 2, Springer, Berlin, Heidelberg, New York, 1972. 7. Cernikov S.N. Groups with prescribed properties of system of subgroups, Nauka, Moskow, 1980. (in Russian) 8. Sunkov V.P. On abstractive properties of some linear groups in Algebra, matrices and matrices groups, Krasnoyarsk, 1970, pp. 5-54. (in Russian) 9. Artemovych O.D. Groups with the minimal condition on non-``nilpotent-by-finite'' subgroups, Serdica Math. J. 28 (2002), 153--162. 10. Harthley B. and McDougall D. Injective modules and soluble groups satisfying the minimal condition for normal subgroups, Bull. Austral. Math. Soc. 4 (1971), 113--135. 11. Asar A.O. On non-nilpotent $p$-groups and the normalizer condition, Turkish J. Math. 18 (1994), 114--129. 12. Maxson C.J. Rigid rings, Proc. Edinburgh Math. Soc. 21 (1979), 95--101. |
| Pages |
215-219
|
| Volume |
22
|
| Issue |
2
|
| Year |
2004
|
| Journal |
Matematychni Studii
|
| Full text of paper | |
| Table of content of issue |