On the Exact Order of Asymptotic Bases and Bases for Finite Cyclic Groups

For a sequence of independent, identically distributed random variable (iid rv's) [Formula: see text] and a sequence of integer-valued random variables [Formula: see text], define the random quantiles as [Formula: see text], where [Formula: see text] denote the largest integer less than or equal to [Formula: see text], and [Formula: see text] the [Formula: see text]th order statistic in a sample [Formula: see text] and [Formula: see text]. In this note, the limiting distribution and its exact order approximation are obtained for [Formula: see text]. The limiting distribution result we obtain extends the work of several including Wretman[Formula: see text]. The exact order of normal approximation generalizes the fixed sample size results of Reiss[Formula: see text]. AMS 2000 subject classification: 60F12; 60F05; 62G30.

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

Journal of Group Theory ◽

10.1515/jgth-2019-0140 ◽

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.

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Exact Order Reduction for the Fornasini-Marchesini State-Space Model Based on Common Invariant Subspace

2019 IEEE International Symposium on Circuits and Systems (ISCAS) ◽

10.1109/iscas.2019.8702558 ◽

2019 ◽

Author(s):

Dongdong Zhao ◽

Shi Yan ◽

Shinya Matsushita ◽

Li Xu

Keyword(s):

State Space ◽

Invariant Subspace ◽

State Space Model ◽

Order Reduction ◽

Exact Order ◽

Space Model ◽

Model Based

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

Duke Mathematical Journal ◽

10.1215/00127094-3450752 ◽

2016 ◽

Vol 165 (9) ◽

pp. 1753-1813 ◽

Cited By ~ 4

Author(s):

Mark F. Hagen ◽

Daniel T. Wise

Keyword(s):

Cyclic Groups

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The Segal Conjecture for Cyclic Groups

Bulletin of the London Mathematical Society ◽

10.1112/blms/13.1.42 ◽

1981 ◽

Vol 13 (1) ◽

pp. 42-44 ◽

Cited By ~ 6

Author(s):

Douglas C. Ravenel

Keyword(s):

Cyclic Groups

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On connectedness of power graphs of finite groups

Journal of Algebra and Its Applications ◽

10.1142/s0219498818501840 ◽

2018 ◽

Vol 17 (10) ◽

pp. 1850184 ◽

Cited By ~ 8

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.

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