On some properties of pronormal subgroups

• Autorzy: Leonid Kurdachenko , Alexsandr Pypka , Igor Subbotin
• Języki publikacji: EN

Abstrakty

EN

New results on tight connections among pronormal, abnormal and contranormal subgroups of a group have been established. In particular, new characteristics of pronormal and abnormal subgroups have been obtained.

Słowa kluczowe

EN

Contranormal subgroup; Pronormal subgroup; Abnormal subgroup; Radical group; Soluble group; Ñ-group

Kategorie tematyczne

• 20F22: Other classes of groups defined by subgroup chains
• 20E15: Chains and lattices of subgroups, subnormal subgroups
• 20F16: Solvable groups, supersolvable groups
• 20F14: Derived series, central series, and generalizations
• 20F19: Generalizations of solvable and nilpotent groups

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 5
• Strony: 840-845

Daty

wydano

2010-10-01

online

2010-09-28

Twórcy

autor

Leonid Kurdachenko

• National University of Dnepropetrovsk

autor

Alexsandr Pypka

• National University of Dnepropetrovsk

autor

Igor Subbotin

• National University

Bibliografia

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• [3] Hall P., On the system normalizers of a soluble group, Proc. Lond. Math. Soc., 1937, 43, 507–528 http://dx.doi.org/10.1112/plms/s2-43.6.507
• [4] Kargapolov M.I., Merzlyakov Yu.I., Fundamentals of the Theory of Groups, Springer, New York, 1979
• [5] Kurdachenko L.A., Otal J., Subbotin I.Ya., Abnormal, pronormal, contranormal, and Carter subgroups in some generalized minimax groups, Comm. Algebra, 2005, 33(12), 4595–4616 http://dx.doi.org/10.1080/00927870500276551
• [6] Kurdachenko L.A., Subbotin I.Ya., Abnormal subgroups and Carter subgroups in some infinite groups, Algebra Discrete Math., 2005, 1, 69–83
• [7] Peng T.A., Pronormality in finite groups, J. Lond. Math. Soc. (2), 1971, 3, 301–306 http://dx.doi.org/10.1112/jlms/s2-3.2.301
• [8] Rose J.S., Nilpotent subgroups of finite soluble groups, Math. Z., 1968, 106, 97–112 http://dx.doi.org/10.1007/BF01110717
• [9] Vincenzi G., Kurdachenko L.A., Russo A., On some groups all subgroups of which are near to pronormal, Ukrainian Math. J., 2007, 59(10), 1493–1500 http://dx.doi.org/10.1007/s11253-008-0007-x
• [10] Wilson J.S., On periodic generalized nilpotent groups, Bull. Lond. Math. Soc., 1977, 9, 81–85 http://dx.doi.org/10.1112/blms/9.1.81
• [11] Wood G.J., On pronormal subgroups of finite soluble groups, Arch. Math. (Basel), 1974, 25, 578–585

Identyfikatory

DOI

10.2478/s11533-010-0051-2