×

zbMATH — the first resource for mathematics

Products of mutually permutable subgroups. (Italian. English summary) Zbl 1162.20309
Summary: We study groups \(G=HK\) admitting a factorization by two mutually sn-permutable subgroups \(H\) and \(K\). Some results of J. C. Beidleman, A. Galoppo, H. Heineken and M. Manfredino [Forum Math. 13, No. 4, 569-580 (2001; Zbl 0984.20016)] are improved.
MSC:
20E15 Chains and lattices of subgroups, subnormal subgroups
20F16 Solvable groups, supersolvable groups
20D40 Products of subgroups of abstract finite groups
20E22 Extensions, wreath products, and other compositions of groups
20F14 Derived series, central series, and generalizations for groups
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] B. AMBERG - S. FRANCIOSI - F. DE GIOVANNI, Products of groups, Clarendon Press, Oxford (1992). Zbl0774.20001 MR1211633 · Zbl 0774.20001
[2] J. C. BEIDLEMAN - A. GALOPPO - H. HEINEKEN - M. MANFREDINO, On certain products of soluble groups, Forum Math., 13 (2001), pp. 569-580. Zbl0984.20016 MR1830247 · Zbl 0984.20016 · doi:10.1515/form.2001.022
[3] J. C. LENNOX, On the solubility of a product of permutable subgroups, J. Austral. Math. Soc., 22 (1976), pp. 252-255. Zbl0342.20016 MR422423 · Zbl 0342.20016
[4] D. J. S. ROBINSON, Finiteness conditions and generalized soluble groups, Springer-Verlag, New York-Heidelberg-Berlin (1972). Zbl0243.20033 · Zbl 0243.20033
[5] S. E. STONEHEWER, Permutable subgroups of infinite groups, Math. Z., 125 (1972), pp. 1-16. Zbl0219.20021 MR294510 · Zbl 0219.20021 · doi:10.1007/BF01111111 · eudml:171686
[6] S. E. STONEHEWER, Permutable subgroups of some finite p-groups, J. Austral. Math. Soc., 16 (1973), pp. 90-97. Zbl0279.20017 MR332964 · Zbl 0279.20017 · doi:10.1017/S1446788700013975
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.