The method of Walker and Wood is used to completely determine the nilpotence height of the elements P s t in the Steenrod algebra at the prime 2. In particular, it is shown that (P s t ) 2bs/tc+2 = 0 for all s ≥ 0, t ≥ 1. In addition, several interesting relations in A are developed in order to carry out the proof.

In the first part of this paper we prove without using the transfer or characters the equivalence of some conditions, each of which would imply p-nilpotence of a finite group G. The implication of p-nilpotence also can be deduced without the transfer or characters if the group is p-constrained. For p-constrained groups we also prove an equivalent condition so that O ′ (G)P should be p-nilpotent...

We prove that if G is a finite 2-generated p-group of nilpotence class at most 2 then the group algebra with coefficients in field p elements determines up to isomorphisms.

Let G be a finite p-group. We say that G has a Johnson polynomial if there exists a polynomial f(x) ∈ Q[x] and a character χ ∈ Irr(G) so that f(χ) equals the total character for G. In this paper, we show that if G has nilpotence class 2, then G has a Johnson polynomial if and only if Z(G) is cyclic, and we show that if |cd(G)| = 2, then G has a Johnson polynomial if and only if G has nilpotence...

In this paper the authors discuss a relationship between ÿnite semiÿelds of characteristic p and certain ÿnite p-groups of nilpotence class 2.

In this paper, the smallest such integer k is called by the index (of nilpotence) of B such that B = 0. In this paper, we study sign patterns allowing nilpotence of index k and obtain four methods to construct sign patterns allowing nilpotence of index at most k, which generalizes some recent results.

In this paper, we find a condition that characterizes when two Camina p-groups of nilpotence class 2 form a Brauer pair. MSC primary: 20C15