The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group

• Autorzy: Leonid Kurdachenko , Javier Otal
• Języki publikacji: EN

Abstrakty

EN

We compare the special rank of the factors of the upper central series and terms of the lower central series of a group. As a consequence we are able to show some generalizations of a theorem of Reinhold Baer.

Słowa kluczowe

EN

Upper central series; Lower central series; Schur theorem; Baer theorem; Finite special rank; Generalized radical group; Hypercentral group

Kategorie tematyczne

• 20F99: None of the above, but in this section
• 20F14: Derived series, central series, and generalizations
• 20F19: Generalizations of solvable and nilpotent groups

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 10
• Strony: 1732-1741

Daty

wydano

2013-10-01

online

2013-07-20

Twórcy

autor

Leonid Kurdachenko

• Department of Algebra, National University of Dnepropetrovsk, 72 Gagarin Av., 49010, Dnepropetrovsk, Ukraine

autor

Javier Otal

• Department of Mathematics — IUMA, University of Zaragoza, Pedro Cerbuna 12, 50009, Zaragoza, Spain

Bibliografia

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• [9] Makarenko N.Yu., Rank analogues of Hall’s and Baer’s theorems, Siberian Math. J., 2000, 41(6), 1137–1140 http://dx.doi.org/10.1023/A:1004828422007[Crossref]
• [10] Schur J., Über die Darstellungen der endlichen Gruppen durch gebrochene lineare substitutionen, J. Reine Angew. Math., 1904, 127, 20–50
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Identyfikatory

DOI

10.2478/s11533-013-0284-y