Some new characteristic p-functors and thompson’s critical subgroup


Kızmaz M. Y.

Communications in Algebra, vol.52, no.2, pp.473-478, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 52 Issue: 2
  • Publication Date: 2024
  • Doi Number: 10.1080/00927872.2023.2243511
  • Journal Name: Communications in Algebra
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.473-478
  • Keywords: Characteristic p-functor, critical subgroup
  • Middle East Technical University Affiliated: Yes

Abstract

Let p be a prime and P be a finite p-group. We define a new characteristic subgroup (Formula presented.) of P and show that (Formula presented.) is a critical subgroup of P. Secondly, we define several new characteristic subgroups (Formula presented.), (Formula presented.) for each positive integer i and show that they enjoy some interesting and new properties similar to the those of critical subgroups. Lastly, for a solvable group G, we define a new characteristic subgroup (Formula presented.), which satisfies the analogue of Thompson’s result for solvable groups.