Al-Sharo, Kahled A.; Beidleman, James C.; Heineken, Hermann; Ragland, Mathew F. Some characterizations of finite groups in which semipermutability is a transitive relation. (English) Zbl 1205.20025 Forum Math. 22, No. 5, 855-862 (2010); corrigendum ibid. 24, No. 6, 1333-1334 (2012). Let \(G\) be a finite group and let \(H\) a subgroup of \(G\); \(H\) is said to be semipermutable in \(G\) if \(H\) permutes with every subgroup of \(G\) with \((|H|,|K|)=1\). A group \(G\) is called a BT-group if semipermutability is a transitive relation in \(G\). The main aim of this paper is to provide some new characterizations of finite solvable BT-groups. In particular, it is proved (Theorem C) that a finite group \(G\) is a solvable BT-group if and only if it has a normal subgroup \(N\) such that \(N\) and \(G/N''\) are solvable BT-groups. Reviewer: Enrico Jabara (Venezia) Cited in 1 ReviewCited in 20 Documents MSC: 20D40 Products of subgroups of abstract finite groups 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks 20D20 Sylow subgroups, Sylow properties, \(\pi\)-groups, \(\pi\)-structure 20D35 Subnormal subgroups of abstract finite groups Keywords:permutability conditions; subnormal subgroups; Sylow bases; system normalizers; transitive semipermutability; semipermutable subgroups; finite solvable groups PDFBibTeX XMLCite \textit{K. A. Al-Sharo} et al., Forum Math. 22, No. 5, 855--862 (2010; Zbl 1205.20025) Full Text: DOI References: [1] DOI: 10.2307/2040211 · Zbl 0299.20014 · doi:10.2307/2040211 [2] DOI: 10.1016/j.jalgebra.2007.12.001 · Zbl 1148.20013 · doi:10.1016/j.jalgebra.2007.12.001 [3] DOI: 10.1017/S0004972700019948 · Zbl 0999.20012 · doi:10.1017/S0004972700019948 [4] DOI: 10.1006/jabr.2001.9138 · Zbl 1010.20013 · doi:10.1006/jabr.2001.9138 [5] DOI: 10.1007/s00013-005-1200-2 · Zbl 1103.20015 · doi:10.1007/s00013-005-1200-2 [6] DOI: 10.1016/j.jalgebra.2005.06.009 · Zbl 1104.20024 · doi:10.1016/j.jalgebra.2005.06.009 [7] DOI: 10.1515/jgth.1999.027 · Zbl 0941.20026 · doi:10.1515/jgth.1999.027 [8] DOI: 10.1016/j.jalgebra.2009.01.007 · Zbl 1190.20015 · doi:10.1016/j.jalgebra.2009.01.007 [9] DOI: 10.1007/BF01195169 · Zbl 0102.26802 · doi:10.1007/BF01195169 [10] DOI: 10.2307/2035343 · Zbl 0159.31002 · doi:10.2307/2035343 [11] Li Y., Internat. J. Algebra 2 pp 143– (2008) [12] Wang L., Acta Math. Sinica 48 pp 81– (2005) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.