Knapsack problem for nilpotent groups

The isomorphism problem for residually torsion-free nilpotent groups

Both the conjugacy and isomorphism problems for finitely generated nilpotent groups are recursively solvable. In some recent work, the first author, with a tiny modification of work in the second author’s thesis, proved that the conjugacy problem for finitely presented, residually torsion-free nilpotent groups is recursively unsolvable. Here we complete the algorithmic picture by proving that t...

The Inverse Galois Problem for Nilpotent Groups of Odd Order

Consider any nilpotent group G of finite odd order. We ask if we can always find a galois extension K of Q such that Gal(K/Q) ∼= G. This is the famous Inverse Galois Problem applied to nilpotent groups of finite odd order. By solving the Group Extension Problem and the Embedding Problem, two problems that are related to the Inverse Galois Problem, we show that such a K always exists. A major re...

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 · ...

Some Inequalities for Nilpotent Multipliers of Powerful p-Groups

Isoperimetric inequalities for nilpotent groups

We prove that every finitely generated nilpotent group of class c admits a polynomial isoperimetric function of degree c+1 and a linear upper bound on its filling length function. 1991 Mathematics Subject Classification: 20F05, 20F32, 57M07