Groups Satisfying Weak Chain Conditions on Certain Non-Normal Subgroups
De Mari, Fausto
Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007), p. 853-866 / Harvested from Biblioteca Digitale Italiana di Matematica

In this paper, (generalized) soluble groups for which the set of all subgroups having infinite index in their normal closure satisfies some weak chain condition are described.

In questo articolo si considerano gruppi risolubili (generalizzati) che verificano una condizione di catena debole sui sottogruppi che non hanno indice finito nella loro chiusura normale.

Publié le : 2007-10-01
@article{BUMI_2007_8_10B_3_853_0,
     author = {Fausto De Mari},
     title = {Groups Satisfying Weak Chain Conditions on Certain Non-Normal Subgroups},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {10-A},
     year = {2007},
     pages = {853-866},
     zbl = {1184.20027},
     mrnumber = {2507901},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_3_853_0}
}
De Mari, Fausto. Groups Satisfying Weak Chain Conditions on Certain Non-Normal Subgroups. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 853-866. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_3_853_0/

[1] Amberg, B., Fast-Polyminimaxgruppen, Math. Ann., 175 (1968), 44-49. | MR 223454

[2] Baer, R., Polyminimaxgruppen, Math. Ann., 175 (1968), 1-43. | MR 223453

[3] Carin, V. S., On soluble groups of type A3, Mat. Sb., 54 (1961), 489-499. | MR 138685

[4] Cutolo, G. - Kurdachenko, L. A., Weak chain conditions for non-almost normal subgroups, Proceedings of Groups St. Andrews in Galway, Cambridge University Press (1993), 120-130. | MR 1342785 | Zbl 0843.20020

[5] De Mari, F. - De Giovanni, F., Double chain conditions for infinite groups, Ricerche Mat., 54 (2005), 59-70. | MR 2290204 | Zbl 1142.20010

[6] Franciosi, S. - De Giovanni, F., Groups satisfying the minimal condition on certain non-normal subgroups, Proceedings of Groups Korea 1994, de Gruyter (1995), 107-118. | MR 1476951 | Zbl 0868.20031

[7] Galoppo, A., Groups satisfying the maximal condition on non-nearly normal subgroups, Ricerche Mat., 49 (2000), 213-220. | MR 1848347 | Zbl 1163.20308

[8] Neumann, B. H., Groups with finite classes of conjugate subgroups, Math Z., 63 (1955), 76-96. | MR 72137 | Zbl 0064.25201

[9] Robinson, D. J. S., Finiteness Conditions and Generalized Soluble Groups, Springer, Berlin (1972). | MR 332990 | Zbl 0243.20032

[10] Shores, T. S., A chain condition for groups, Rocky Mountain J. Math., 3 (1973), 83-89. | MR 347984 | Zbl 0256.20034

[11] Šunkov, V. P., Locally finite groups with a minimality condition for abelian subgroups, Algebra and Logic, 9 (1970), 350-370. | MR 283063

[12] Zaičev, D. I., Groups satisfying a weak minimum condition, Soviet Math. Dokl., 9 (1968), 194-197.

[13] Zaičev, D. I., On groups which satisfy a weak minimality condition, Math. USSR Sb., 7 (1969), 315-322.

[14] Zaičev, D. I., Theory of minimax groups, Ukrainian Math. J., 23 (1971), 536-542.