Nilpotent residual and Fitting subgroup of fixed points in finite groups
| Autor: | Emerson de Melo |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Algebra and Number Theory
010102 general mathematics Order (ring theory) Group Theory (math.GR) Fixed point Automorphism 01 natural sciences Fitting subgroup Prime (order theory) Combinatorics Nilpotent Bounded function 0103 physical sciences Exponent FOS: Mathematics 010307 mathematical physics 0101 mathematics Mathematics - Group Theory Mathematics |
| DOI: | 10.48550/arxiv.1903.01440 |
| Popis: | Let $q$ be a prime and $A$ a finite $q$-group of exponent $q$ acting by automorphisms on a finite $q'$-group $G$. Assume that $A$ has order at least $q^3$. We show that if $\gamma_{\infty} (C_{G}(a))$ has order at most $m$ for any $a \in A^{\#}$, then the order of $\gamma_{\infty} (G)$ is bounded solely in terms of $m$. If the Fitting subgroup of $C_{G}(a)$ has index at most $m$ for any $a \in A^{\#}$, then the second Fitting subgroup of $G$ has index bounded solely in terms of $m$. Comment: arXiv admin note: substantial text overlap with arXiv:1810.05663 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|