FITTING SUBGROUP AND NILPOTENT RESIDUAL OF FIXED POINTS
| Autor: | Pavel Shumyatsky, Emerson de Melo |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
General Mathematics
010102 general mathematics Order (ring theory) Elementary abelian group Group Theory (math.GR) 0102 computer and information sciences Fixed point Automorphism 01 natural sciences Fitting subgroup Prime (order theory) Combinatorics Nilpotent 010201 computation theory & mathematics FOS: Mathematics 0101 mathematics Mathematics - Group Theory Mathematics |
| Zdroj: | Bulletin of the Australian Mathematical Society. 100:61-67 |
| ISSN: | 1755-1633 0004-9727 |
| DOI: | 10.1017/s0004972718001272 |
| Popis: | Let $q$ be a prime and $A$ an elementary abelian group of order at least $q^3$ acting by automorphisms on a finite $q'$-group $G$. It is proved that if $|\gamma_{\infty}(C_{G}(a))|\leq m$ for any $a\in A^{\#}$, then the order of $\gamma_{\infty}(G)$ is $m$-bounded. If $F(C_{G}(a))$ has index at most $m$ in $C_G(a)$ for any $a \in A^{\#}$, then the index of $F_2(G)$ is $m$-bounded. Comment: arXiv admin note: text overlap with arXiv:1712.08103 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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