Extremal Functions on Cayley Digraphs of Finite Cyclic Groups

2012 ◽  
Author(s):  
Jordan F. Blocher ◽  
Samantha M. Hampton ◽  
Christopher E. Linden
Keyword(s):  
Extremal Functions ◽  
Cyclic Groups

scholarly journals On the Boundary Dieudonné–Pick Lemma

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1108
Author(s):  
Olga Kudryavtseva ◽  
Aleksei Solodov
Keyword(s):  
Fixed Point ◽  
Interior Point ◽  
Sharp Estimate ◽  
General Boundary ◽  
Extremal Functions ◽  
Angular Derivative ◽  
Additional Information ◽  
Carathéodory Theorem ◽  
Class Of Functions ◽  
Boundary Fixed Point

The class of holomorphic self-maps of a disk with a boundary fixed point is studied. For this class of functions, the famous Julia–Carathéodory theorem gives a sharp estimate of the angular derivative at the boundary fixed point in terms of the image of the interior point. In the case when additional information about the value of the derivative at the interior point is known, a sharp estimate of the angular derivative at the boundary fixed point is obtained. As a consequence, the sharpness of the boundary Dieudonné–Pick lemma is established and the class of the extremal functions is identified. An unimprovable strengthening of the Osserman general boundary lemma is also obtained.

On the minimal varieties of PI-algebras graded by finite cyclic groups

2021 ◽  
pp. 1-25
Author(s):  
Marcos Antônio da Silva Pinto ◽  
Viviane Ribeiro Tomaz da Silva
Keyword(s):  
Cyclic Groups

scholarly journals Initial logarithmic coefficients for functions starlike with respect to symmetric points

2021 ◽  
Vol 27 (3) ◽  
Author(s):  
Paweł Zaprawa
Keyword(s):  
Exact Result ◽  
Positive Real Part ◽  
Additional Benefit ◽  
Extremal Functions ◽  
Positive Real ◽  
Logarithmic Coefficients ◽  
Symmetric Points

AbstractIn this paper, we obtain the bounds of the initial logarithmic coefficients for functions in the classes $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S of functions which are starlike with respect to symmetric points and convex with respect to symmetric points, respectively. In our research, we use a different approach than the usual one in which the coeffcients of f are expressed by the corresponding coeffcients of functions with positive real part. In what follows, we express the coeffcients of f in $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S by the corresponding coeffcients of Schwarz functions. In the proofs, we apply some inequalities for these functions obtained by Prokhorov and Szynal, by Carlson and by Efraimidis. This approach offers a additional benefit. In many cases, it is easily possible to predict the exact result and to select extremal functions. It is the case for $${\mathcal {S}}_S^*$$ S S ∗ and $${\mathcal {K}}_S$$ K S .

scholarly journals Serre’s Property (FA) for automorphism groups of free products

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Naomi Andrew
Keyword(s):  
Automorphism Group ◽  
Free Product ◽  
Finite Groups ◽  
Automorphism Groups ◽  
Sufficient Conditions ◽  
Free Products ◽  
Cyclic Groups ◽  
Link Type ◽  
Open Case

AbstractWe provide some necessary and some sufficient conditions for the automorphism group of a free product of (freely indecomposable, not infinite cyclic) groups to have Property (FA). The additional sufficient conditions are all met by finite groups, and so this case is fully characterised. Therefore, this paper generalises the work of N. Leder [Serre’s Property FA for automorphism groups of free products, preprint (2018), https://arxiv.org/abs/1810.06287v1]. for finite cyclic groups, as well as resolving the open case of that paper.

scholarly journals Cubulating hyperbolic free-by-cyclic groups: The irreducible case

2016 ◽  
Vol 165 (9) ◽  
pp. 1753-1813 ◽  
Author(s):  
Mark F. Hagen ◽  
Daniel T. Wise
Keyword(s):  
Cyclic Groups

scholarly journals The Segal Conjecture for Cyclic Groups

1981 ◽  
Vol 13 (1) ◽  
pp. 42-44 ◽  
Author(s):  
Douglas C. Ravenel
Keyword(s):  
Cyclic Groups

scholarly journals On connectedness of power graphs of finite groups

2018 ◽  
Vol 17 (10) ◽  
pp. 1850184 ◽  
Author(s):  
Ramesh Prasad Panda ◽  
K. V. Krishna
Keyword(s):  
Finite Groups ◽  
Upper Bound ◽  
The Other ◽  
Number Of Components ◽  
Cyclic Groups ◽  
Power Graph ◽  
Vertex Set ◽  
Proper Power

The power graph of a group [Formula: see text] is the graph whose vertex set is [Formula: see text] and two distinct vertices are adjacent if one is a power of the other. This paper investigates the minimal separating sets of power graphs of finite groups. For power graphs of finite cyclic groups, certain minimal separating sets are obtained. Consequently, a sharp upper bound for their connectivity is supplied. Further, the components of proper power graphs of [Formula: see text]-groups are studied. In particular, the number of components of that of abelian [Formula: see text]-groups are determined.

scholarly journals Higher K -theory of group-rings of virtually infinite cyclic groups

2003 ◽  
Vol 325 (4) ◽  
pp. 711-726 ◽  
Author(s):  
Aderemi O. Kuku ◽  
Guoping Tang
Keyword(s):  
Group Rings ◽  
Cyclic Groups ◽  
K Theory
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