The structure of (non-periodic) groups in which all non-periodic subgroups have a prescribed property is investigated. Among other choices, we consider properties generalizing normality, like subnormality, permutability and pronormality. Moreover, non-periodic groups whose proper non-periodic subgroups belong to a given group class are studied.
@article{BUMI_2011_9_4_1_109_0,
author = {Maria De Falco and Francesco de Giovanni and Carmela Musella},
title = {Groups with Normality Conditions for Non-Periodic Subgroups},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {4},
year = {2011},
pages = {109-121},
zbl = {1238.20043},
mrnumber = {2797468},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2011_9_4_1_109_0}
}
De Falco, Maria; de Giovanni, Francesco; Musella, Carmela. Groups with Normality Conditions for Non-Periodic Subgroups. Bollettino dell'Unione Matematica Italiana, Tome 4 (2011) pp. 109-121. http://gdmltest.u-ga.fr/item/BUMI_2011_9_4_1_109_0/
[1] , Überauflösbare Gruppen, Abh. Math. Sem. Univ. Hamburg, 23 (1957), 11-28. | MR 103925
[2] , Groups with many nearly normal subgroups, Boll. Un. Mat. Ital., 4B (2001), 531-540. | MR 1832003 | Zbl 1147.20302
[3] - - , Groups whose finite homomorphic images are metahamiltonian, Comm. Algebra, 37 (2009), 2468-2476. | MR 2536934 | Zbl 1178.20033
[4] - , Groups with many subgroups having modular subgroup lattice, Ricerche Mat., 51 (2002), 241-247. | MR 2030541 | Zbl 1144.20306
[5] , Minimal nicht überauflösbare, endliche Gruppen, Math. Z., 91 (1966), 198-205. | MR 191962
[6] - , Some topics in the theory of pronormal subgroups of groups, Quaderni Mat., 8 (2001), 175-202. | MR 1949564 | Zbl 1021.20019
[7] - , A group with trivial centre satisfying the normalizer condition, J. Algebra, 10 (1968), 368-376. | MR 235035 | Zbl 0167.29001
[8] - - , Groups with almost normal infinite subgroups, Soviet Math. (izv. VUZ), 27 (1983), 73-81. | MR 729965 | Zbl 0572.20024
[9] - , Structure of solvable nonnilpotent metahamiltonian groups, Math. Notes, 34 (1983), 572-577. | MR 719472 | Zbl 0545.20027
[10] - , Groups in which all subgroups are pronormal, Ukrain. Math. J., 39 (1987), 251-254. | MR 899498 | Zbl 0642.20028
[11] , Auflösbarkeit von Gruppen, deren Untergruppen alle subnormal sind, Arch. Math. (Basel), 54 (1990), 232-235. | MR 1037610
[12] , Polycyclic groups with modular finite homomorphic images, Arch. Math. (Basel), 76 (2001), 161-165. | MR 1816986 | Zbl 0988.20017
[13] , Groups with finite classes of conjugate subgroups, Math. Z., 63 (1955), 76-96. | MR 72137 | Zbl 0064.25201
[14] - , Minimal non-CC-groups, Comm. Algebra, 16 (1988), 1231- 1242. | MR 939041 | Zbl 0644.20025
[15] , Groups in which normality is a transitive relation, Proc. Cambridge Philos. Soc., 60 (1964), 21-38. | MR 159885 | Zbl 0123.24901
[16] , Finiteness Conditions and Generalized Soluble Groups, Springer, Berlin (1972). | MR 332989 | Zbl 0243.20032
[17] , Groups whose homomorphic images have a transitive normality relation, Trans. Amer. Math. Soc., 176 (1973), 181-213. | MR 323907 | Zbl 0272.20020
[18] - , Metahamiltonian groups, Ural. Gos. Univ. Mat. Zap., 5 (1966), 101-106. | MR 202837
[19] - , Metahamiltonian groups II, Ural. Gos. Univ. Mat. Zap., 6 (1968), 52-58. | MR 269733 | Zbl 0351.20021
[20] - , Metahamiltonian groups III, Ural. Gos. Univ. Mat. Zap., 7 (1969/70), 195-199. | MR 285610 | Zbl 0324.20036
[21] , Subgroup Lattices of Groups, de Gruyter, Berlin (1994). | MR 1292462
[22] , Groups with few non-nilpotent subgroups, Glasgow Math. J., 39 (1997), 141-151. | MR 1460630 | Zbl 0883.20018
[23] - , Locally graded groups with all subgroups normal-by-finite, J. Austral. Math. Soc. Ser. A, 60 (1996), 222-227. | MR 1375587 | Zbl 0855.20028
[24] , FC-groups, Pitman, Boston (1984). | MR 742777