Sets of prime power order generators of finite groups

• Date: 2020
• Main Author: Stocka, A.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2020
• Subjects: finite groups; independent sets; minimal generating sets; Burnside basis theorem; Primary 20D10; Secondary 20F05
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1479
• Journal Title: Algebra and Discrete Mathematics

A subset \(X\) of prime power order elements of a finite group \(G\) is called pp-independent if there is no proper subset \(Y\) of \(X\) such that \(\langle Y,\Phi(G) \rangle = \langle X,\Phi(G) \rangle\), where \(\Phi(G)\) is the Frattini subgroup of \(G\). A group \(G\) has property \(\mathcal{B}...