Powerful 2-Engel groups II |
| |
Authors: | Gunnar Traustason |
| |
Institution: | Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK |
| |
Abstract: | We conclude our classification of powerful 2-Engel groups of class three that are minimal in the sense that every proper powerful section is nilpotent of class at most two. In the predecessor to this paper we obtained three families of minimal groups. Here we get a fourth family of minimal examples that is described in terms of irreducible polynomials over the field of three elements. We also get one isolated minimal example of rank 5 and exponent 27. The last one has a related algebraic structure that we call a “symplectic alternating algebra.” To each symplectic alternating algebra over the field of three elements there corresponds a unique 2-Engel group of exponent 27. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|