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Title: On transitivity of pronormality (English)
Author: Kurdachenko, Leonid A.
Author: Subbotin, Igor Ya.
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 43
Issue: 4
Year: 2002
Pages: 583-594
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Category: math
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Summary: This article is dedicated to soluble groups, in which pronormality is a transitive relation. Complete description of such groups is obtained. (English)
Keyword: pronormal subgroups
Keyword: transitive relations
MSC: 20E15
MSC: 20F16
idZBL: Zbl 1068.20036
idMR: MR2045782
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Date available: 2009-01-08T19:25:27Z
Last updated: 2012-04-30
Stable URL: http://hdl.handle.net/10338.dmlcz/119349
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Reference: [AK] Abramovskii I.N., Kargapolov M.I.: Finite groups with the property of transitivity for normal subgroups.Uspekhi Mat. Nauk 13 (1958), 232-243.
Reference: [B] Borevich Z.I.: Polynormal subgroups.Darstellungstheorietage (Erfurt, 1992), pp.7-19, Sitzungsber. Mat.-Naturwiss. KI., 4 Acad. Gemein. Wiss. Erfurt, Erfurt, 1992. Zbl 0807.20026, MR 1225383
Reference: [BB] Ba M.S., Borevich Z.I.: On arrangement of intermediate subgroups.Rings and Linear Groups, Kubansk. Univ., Krasnodar, 1988, pp.14-41. MR 1206023
Reference: [BT] Best E., Taussky O.: A class of groups.Proc. Roy. Irish Acad. Sect. A 47 (1942), 55-62. Zbl 0063.00359, MR 0006539
Reference: [C] Carter R.W.: Nilpotent self-normalizing subgroups of soluble groups.Math. Z. 75 (1961), 136-139. Zbl 0168.27301, MR 0123603
Reference: [Ce] Celentani M.R.: On groups with many pronormal subgroups.Atti Sem. Mat. Fis. Univ. Modena 39 (1991), 2 685-691. Zbl 0807.20033, MR 1150808
Reference: [CD] Celentani M.R., Dardano U.: Some sensitivity conditions for infinite groups.Rend. Mat. Appl. (7) 12 (1992), 4 997-1012. Zbl 0774.20017, MR 1218600
Reference: [deGV] De Giovanni F., Vincenzi G.: Groups satisfying the minimal condition on non-pronormal subgroups.Boll. Un. Mat. Ital. A (7) 9 (1995), 185-194. Zbl 0837.20040, MR 1324619
Reference: [deFKS] De Falco M., Kurdachenko L.A., Subbotin I.Ya.: Groups with only abnormal and subnormal subgroups.Atti Sem. Mat. Fis. Univ. Modena 46 2 (1998), 435-442. Zbl 0918.20017, MR 1665935
Reference: [E1] Emaldi E.: Sui T-gruppi loclmente finiti.Atti Istit. Lombardo (Rend. Sci.) A 121 (1987), 55-60.
Reference: [E2] Emaldi E.: Confronto di alcule classi gruppali.Riv. Mat. Pura Appl. 5 (1989), 33-39.
Reference: [F] Fatahi A.: Groups with only normal and abnormal subgroups.J. Algebra 28 (1974), 15-19. MR 0335628
Reference: [FdeG] Fransiosi S., De Giovanni F.: Groups in which every infinite subnormal subgroups is normal.J. Algebra 96 (1985), 566-580. MR 0810546
Reference: [G] Gaschutz W.: Gruppen in denen das Normalteilersein transitive ist.J. Reine Angew. Math. 198 (1957), 87-92. MR 0091277
Reference: [GK] Gavron P.V., Kolotilina N.Yu.: On subgroups of T-groups.Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 103 (1980), 62-65. MR 0618496
Reference: [H] Heineken H., Lennox J.C.: Subgroups of finite index in T-groups.Boll. Un. Mat. Ital. B (6) 4 3 (1985), 829-841. Zbl 0598.20027, MR 0831294
Reference: [HL] Heineken H.: Groups with restriction on their infinite subnormal subgroups.Proc. Edinburg Math. Soc. 31 (1988), 231-241. Zbl 0644.20020, MR 0989756
Reference: [KS1] Kuzennyi N.F, Subbotin I.Ya.: Locally soluble groups with the transitive condition for infinite nonabelian normal subgroups.Methods of Investigations of Algebraic and Topologic Structures, Kiev State Pedagogic University, Kiev, 1989, pp.45-52.
Reference: [KS2] Kuzennyi N.F, Subbotin I.Ya.: Groups in which all subgroups are pronormal.Ukrain. Mat. Zh. 39 (1987), 325-329; English translation: Ukrainian Math. J. 39 (1987), 251-254. MR 0899498
Reference: [KS3] Kuzennyi N.F, Subbotin I.Ya.: Groups with pronormal primary subgroups.Ukrain. Mat. Zh. 41 (1989), 323-327; English translation: Ukrainian Math. J. 41 (1989), 286-289. MR 1001537
Reference: [KS4] Kuzennyi N.F, Subbotin I.Ya.: New characterization of locally nilpotent $øverline{IH}$-groups.Ukrain. Mat. Zh. 40 (1988), 322-326; English translation: Ukrainian Math. J. 40 (1988), 274-277. MR 0952119
Reference: [KS5] Kuzennyi N.F, Subbotin I.Ya.: On nonsplittable group extensions.Studies of Groups with Restrictions on Subgroups, Inst. of Math. of Acad. Sci. Ukraine, Kiev, 1988, pp.27-33. MR 0988170
Reference: [M1] Menegazzo F.: Gruppi nei quail la relazone di quasi-normalita e tranzitiva.Rend. Sem. Mat. Univ. Padova 40 (1968), 347-361. MR 0228584
Reference: [M2] Menegazzo F.: Gruppi nei quail la relazone di quasi-normalita e tranzitiva II.Rend. Sem. Mat. Univ. Padova 42 (1969), 389-399. MR 0257225
Reference: [Mu] Müller K.H.: Schwachnormale Untergruppen: Eine gemeinsame Verallgemeinerung der normalen und normalizatorgleichen Untergruppen.Rend. Sem. Mat. Univ. Padova 36 (1966), 129-157. MR 0204528
Reference: [P] Peng T.A.: Pronormality in finite groups.J. London Math. Soc. (2) 3 (1971), 301-306. Zbl 0209.05502, MR 0276319
Reference: [R1] Robinson D.J.S.: Groups in which normality is a transitive relation.Proc. Cambridge Philos. Soc. 60 (1964), 21-38. Zbl 0123.24901, MR 0159885
Reference: [R2] Robinson D.J.S.: A note on finite groups in which normality is transitive.Proc. Amer. Math. Soc. 19 (1968), 933-937. Zbl 0159.31002, MR 0230808
Reference: [R3] Robinson D.J.S.: Groups which are minimal with respect to normality being transitive.Pacific J. Math. 31 (1969), 777-785. MR 0258943
Reference: [R4] Robinson D.J.S.: Groups whose gomomorphic images have a transitive normality relation.Trans. Amer. Math. Soc. 176 (1973), 181-213. MR 0323907
Reference: [Ro] Rose J.S.: Finite soluble groups with pronormal system normalizers.Proc. London Math. Soc. (3) 17 (1967), 447-469. Zbl 0153.03602, MR 0212092
Reference: [S1] Subbotin I.Ya.: Groups with pronormal subgroups of proper normal subgroups.in Proceedings of International Conference ``Infinite Groups 1994'', Walter der Gruyter, Berlin, 1995, pp.247-256. Zbl 0866.20028, MR 1477182
Reference: [SK] Subbotin I.Ya, Kuzennyi N.F.: Locally solvable groups in which all infinite subgroups are pronormal.Izv. Vyssh. Ucheb. Zaved. Mat. 11 (1988), 77-79; English translation: Soviet. Math. 32 (1988), no. 11, 126-131. MR 0983287
Reference: [V] Vincenzi G.: Groups with dense pronormal subgroups.Ricerche Mat. XL (1991), 75-79. Zbl 0754.20011, MR 1191887
Reference: [V1] Vincenzi G.: Groups satisfying the maximall condition on non-pronormal subgroups.Algebra Colloq. 5:2 (1998), 121-134. MR 1682978
Reference: [W] Wood G.J.: On pronormal subgroups of finite soluble groups.Arch. Math. 25 (1974), 578-585. Zbl 0301.20011, MR 0379660
Reference: [Z] Zacher G.: Caratterizzazione dei t-gruppi finite risolubili.Ricerche Mat. 1 (1952), 287-294. MR 0053104
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