Nilpotent groups are not dualizable

Groups that are pairwise nilpotent

In this paper we study groups generated by a set X with the property that every two elements in X generate a nilpotent subgroup.

Z8 Is Not Dualizable

An Algebra That Is Dualizable but Not Fully Dualizable

We give an example of a finite algebra which is dualizable but not fully dualizable in the sense of natural duality theory.

4-Engel Groups are Locally Nilpotent

Questions about nilpotency of groups satisfying Engel conditions have been considered since 1936, when Zorn proved that finite Engel groups are nilpotent. We prove that 4-Engel groups are locally nilpotent. Our proof makes substantial use of both hand and machine calculations.

Nilpotent Groups

The articles [2], [3], [4], [6], [7], [5], [8], [9], [10], and [1] provide the notation and terminology for this paper. For simplicity, we use the following convention: x is a set, G is a group, A, B, H, H1, H2 are subgroups of G, a, b, c are elements of G, F is a finite sequence of elements of the carrier of G, and i, j are elements of N. One can prove the following propositions: (1) ab = a · ...