scholarly journals Nilpotent residual of fixed points

2018 ◽  
Vol 111 (1) ◽  
pp. 13-21 ◽  
Author(s):  
Emerson de Melo ◽  
Aline de Souza Lima ◽  
Pavel Shumyatsky
Keyword(s):  
Fixed Points ◽  
Nilpotent Residual

scholarly journals FITTING SUBGROUP AND NILPOTENT RESIDUAL OF FIXED POINTS

2018 ◽  
Vol 100 (1) ◽  
pp. 61-67
Author(s):  
EMERSON DE MELO ◽  
PAVEL SHUMYATSKY
Keyword(s):  
Abelian Group ◽  
Fixed Points ◽  
Elementary Abelian Group ◽  
Fitting Subgroup ◽  
Nilpotent Residual ◽  
Formula Group

Let $q$ be a prime and let $A$ be an elementary abelian group of order at least $q^{3}$ acting by automorphisms on a finite $q^{\prime }$-group $G$. We prove that if $|\unicode[STIX]{x1D6FE}_{\infty }(C_{G}(a))|\leq m$ for any $a\in A^{\#}$, then the order of $\unicode[STIX]{x1D6FE}_{\infty }(G)$ 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.

scholarly journals Nilpotent residual and fitting subgroup of fixed points in finite groups

2019 ◽  
Vol 22 (6) ◽  
pp. 1059-1068
Author(s):  
Emerson de Melo
Keyword(s):  
Fixed Points ◽  
Finite Groups ◽  
Fitting Subgroup ◽  
Nilpotent Residual ◽  
Formula Group

Abstract Let q be a prime and A a finite q-group of exponent q acting by automorphisms on a finite {q^{\prime}} -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.

On $\alpha$-nonexpansive mapping and fixed-points in Banach spaces

2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
Prondanai Kaskasem ◽  
Chakkrid Klin-eam ◽  
Suthep Suantai
Keyword(s):  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Banach Spaces

Fixed Points of Sequences of Mappings

2018 ◽  
Vol 2018 (-) ◽  
Author(s):  
C. Ganesa Moorthy ◽  
S. Iruthaya Raj
Keyword(s):  
Fixed Points
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