Cardin, Marta On a class of groups with many quasinormal subgroups. (Italian) Zbl 0597.20022 Rend. Sem. Mat. Univ. Padova 72, 157-161 (1984). The author studies the structure of groups G of the following class: If \(\{H_ i\}_{i\in I}\) is a family of subgroups of G such that \(G=<H_ i:\) \(i\in I>\) then for each i,j\(\in I\), any subgroup contained in \(H_ i\vee H_ j\) is quasinormal in G. It is known that a periodic group with this property is metabelian. The author improves the mentioned result in the following way: If \(\sigma\) is a projectivity of the group G into the group \(\bar G\) and \(N\triangleleft G\), then \((N^{\sigma}[N^{\sigma},2\bar G])^{\sigma -1}/N\) is a modular group. Reviewer: F.Šik MSC: 20E15 Chains and lattices of subgroups, subnormal subgroups 20E07 Subgroup theorems; subgroup growth 20E34 General structure theorems for groups 20E28 Maximal subgroups 06B15 Representation theory of lattices 20F50 Periodic groups; locally finite groups Keywords:quasinormal subgroups; metabelian groups; periodic group; projectivity; modular group PDFBibTeX XMLCite \textit{M. Cardin}, Rend. Semin. Mat. Univ. Padova 72, 157--161 (1984; Zbl 0597.20022) Full Text: Numdam EuDML References: [1] D. Gorenstein , Finite groups , Harper Row ( 1968 ). MR 231903 | Zbl 0185.05701 · Zbl 0185.05701 [2] F. Napolitani - G. Zacher , Über das Verhalten der Normalteiler unter Projektivitaten (in corso di pubbl. su Math. Z. ). Article | MR 706395 | Zbl 0517.20011 · Zbl 0517.20011 · doi:10.1007/BF01176478 [3] D. Robinson , Finiteness conditions and generalized soluble groups , vol. I e II , Springer-Verlag ( 1972 ). Zbl 0243.20033 · Zbl 0243.20033 [4] M. Suzuki , Struoture of a group and the structure of its lattice of subgroups , Springer ( 1956 ). MR 83487 | Zbl 0070.25406 · Zbl 0070.25406 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.