ON NONABELIAN TENSOR ANALOGUES OF 2-ENGEL CONDITIONS

Tensor analogues of right 2-Engel elements in groups were introduced by D. P. Biddle and L.-C. Kappe. We investigate the properties of right 2-Engel tensor elements and introduce the concept of 2(circled times)-Engel margin. With the help of these results we describe the structure of 2(circled times)-Engel groups. In particular, we prove a tensor version of Leviʹs theorem for 2-Engel groups and determine tensor squares of two-generator 2(circled times)-Engel p-groups.