L_{10}-free \{p,q\}-groups


If L is a lattice, a group is called L-free if its subgroup lattice has no sublattice isomorphic to L. It is easy to see that L_{10}, the subgroup lattice of the dihedral group of order 8, is the largest lattice L such that every finite L-free p-group is modular. In this paper we continue the study of L_{10}-free groups. We determine all finite L_{10}-free \{p,q\}-groups for primes p and q, except those of order 2^{\alpha}3^{\beta} with normal Sylow 3-subgroup

DOI Code: 10.1285/i15900932v30n1supplp55

Keywords: subgroup lattice; sublattice; finite group; modular Sylow subgroup

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