Science/Engineering Subgroup Lattices of Groups (De Gruyter Expositions in Mathematics) (3110112132)

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Subgroup Lattices of Groups (De Gruyter Expositions in Mathematics)

Let $G$ be a group. The set L(G) of all subgroups of $G$ ordered by the inclusion set relation is a complete lattice, where for each pair ($H,K)$ of subgroups of $G$ the lower bound of $\{H,K\}$ is the usual intersection $H\cap K$ , and the upper bound of $\{H,K\}$ is the subgroup $\langle H,K\rangle$ generated by $H$ and $K$ . The investigation of the connections between the structure of a group $G$ and that of its subgroup lattice $L(G)$ started in 1928 with a paper of A. Rottländer, and was continued by several authors. Properties of subgroup lattices of groups known by 1956 can be found in the book by M. Suzuki [Structure of a group and the structure of its lattice of subgroups, Springer, Berlin, 1956; MR0083487 (18,715e)]. Since then many new results on this topic have been obtained, and the book under review is an extensive account of this theory.

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