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In this short note we confirm an analog of a conjecture of James Wiegold for finite dimensional nilpotent Lie algebras., 5 pages

In this article, we introduce an algorithm for automatic generation and categorization of triangle geometry theorems., Comment: Improved version

This paper focuses on a new approach to plane geometry and develops important concepts that can allow researchers to unite and observe plane geometry from a new, meaningful perspective.

This work is a continuation of [1]. As in the previous article, here we will describe some interesting ideas and a lot of new theorems in plane geometry related to them., 17 pages, 13 figures

In this short note we confirm a conjecture of James Wiegold. We prove that if $G$ is a finite $p$-group and $|G'|>p^{n(n-1)/2}$ for some non-negative integer $n$, then the group $G$ can be generated by the elements of breadth at least $n$. The breadth $b(x)$ of an element $x$ of a finite $p$-group $G$ is defined by the equation $|G:C_G(x)| = p^{b(x)}$, where $C_G(x)$ is the centralizer of $x$ in $G$., 4 pages

In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry., Comment: 19 pages, 15 figures, replaced some facts, corrected typos, final version