scholarly journals Invariance groups of finite functions and orbit equivalence of permutation groups

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Eszter K. Horváth ◽  
Géza Makay ◽  
Reinhard Pöschel ◽  
Tamás Waldhauser
Keyword(s):  
Symmetric Group ◽  
Partial Answer ◽  
Permutation Groups ◽  
Computational Results ◽  
Orbit Equivalence ◽  
Alternating Groups ◽  
Primitive Groups ◽  
Complete Answer ◽  
The Difference ◽  
Invariance Groups

AbstractWhich subgroups of the symmetric group Sn arise as invariance groups of n-variable functions defined on a k-element domain? It appears that the higher the difference n-k, the more difficult it is to answer this question. For k ≤ n, the answer is easy: all subgroups of Sn are invariance groups. We give a complete answer in the cases k = n-1 and k = n-2, and we also give a partial answer in the general case: we describe invariance groups when n is much larger than n-k. The proof utilizes Galois connections and the corresponding closure operators on Sn, which turn out to provide a generalization of orbit equivalence of permutation groups. We also present some computational results, which show that all primitive groups except for the alternating groups arise as invariance groups of functions defined on a three-element domain.

Bounds for finite semiprimitive permutation groups: order, base size, and minimal degree

2020 ◽  
Vol 63 (4) ◽  
pp. 1071-1091
Author(s):  
Luke Morgan ◽  
Cheryl E. Praeger ◽  
Kyle Rosa
Keyword(s):  
Fixed Point ◽  
Normal Subgroup ◽  
Symmetric Group ◽  
Minimal Normal Subgroup ◽  
Structural Information ◽  
Minimal Degree ◽  
Permutation Groups ◽  
Primitive Groups ◽  
Base Size ◽  
Abstract Structure

AbstractIn this paper, we study finite semiprimitive permutation groups, that is, groups in which each normal subgroup is transitive or semiregular. These groups have recently been investigated in terms of their abstract structure, in a similar way to the O'Nan–Scott Theorem for primitive groups. Our goal here is to explore aspects of such groups which may be useful in place of precise structural information. We give bounds on the order, base size, minimal degree, fixed point ratio, and chief length of an arbitrary finite semiprimitive group in terms of its degree. To establish these bounds, we study the structure of a finite semiprimitive group that induces the alternating or symmetric group on the set of orbits of an intransitive minimal normal subgroup.

Two open problems in the fixed point theory of contractive type mappings on quasimetric spaces

2017 ◽  
Vol 33 (2) ◽  
pp. 169-180
Author(s):  
MITROFAN M. CHOBAN ◽  
◽  
VASILE BERINDE ◽  
◽  
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Partial Answer ◽  
Open Problems ◽  
Complete Answer ◽  
Contractive Type ◽  
Generalized Distances

Two open problems in the fixed point theory of quasi metric spaces posed in [Berinde, V. and Choban, M. M., Generalized distances and their associate metrics. Impact on fixed point theory, Creat. Math. Inform., 22 (2013), No. 1, 23–32] are considered. We give a complete answer to the first problem, a partial answer to the second one, and also illustrate the complexity and relevance of these problems by means of four very interesting and comprehensive examples.

scholarly journals Affine Primitive Groups and Semisymmetric Graphs

10.37236/2549 ◽  
2013 ◽  
Vol 20 (2) ◽  
Author(s):  
Hua Han ◽  
Zaiping Lu
Keyword(s):  
Bipartite Graph ◽  
Complete Bipartite Graph ◽  
Infinite Family ◽  
Permutation Groups ◽  
Primitive Groups ◽  
The Third ◽  
Semisymmetric Graphs

In this paper, we investigate semisymmetric graphs which arise from affine primitive permutation groups. We give a characterization of such graphs, and then construct an infinite family of semisymmetric graphs which contains the Gray graph as the third smallest member. Then, as a consequence, we obtain a factorization,of the complete bipartite graph $K_{p^{sp^t},p^{sp^t}}$ into connected semisymmetric graphs, where $p$ is an prime, $1\le t\le s$ with $s\ge2$ while $p=2$.

Univalence of a complex linear combination of two extremal parallel slit mappings

Analysis ◽  
2007 ◽  
Vol 27 (2-3) ◽  
Author(s):  
Masakazu Shiba
Keyword(s):  
Linear Combination ◽  
Present Article ◽  
Convex Combination ◽  
Plane Domain ◽  
Partial Answer ◽  
Vertical Slit ◽  
Complete Answer ◽  
Conformal Welding ◽  
Parallel Slit ◽  
Complex Linear

Any convex combination of the so-called extremal horizontal and vertical slit mappings of a plane domain is known to be univalent. In his study on the conformal welding of annuli F. Maitani needed to know when a complex linear combination is univalent and he gave a partial answer to this problem. In the present article we give a complete answer to his and to generalized problems.

scholarly journals Derangements in cosets of primitive permutation groups

2015 ◽  
Vol 18 (1) ◽  
Author(s):  
Andrei Pavelescu
Keyword(s):  
Fixed Point ◽  
Finite Fields ◽  
Permutation Groups ◽  
Normal Subgroups ◽  
Primitive Groups ◽  
Branched Coverings ◽  
Affine Groups ◽  
Nonabelian Subgroup ◽  
Projective Curves ◽  
Curves Over Finite Fields

AbstractMotivated by questions arising in connection with branched coverings of connected smooth projective curves over finite fields, we study the proportion of fixed-point free elements (derangements) in cosets of normal subgroups of primitive permutations groups. Using the Aschbacher–O'Nan–Scott Theorem for primitive groups to partition the problem, we provide complete answers for affine groups and groups which contain a regular normal nonabelian subgroup.

scholarly journals Bounds and quotient actions of innately transitive groups

2005 ◽  
Vol 79 (1) ◽  
pp. 95-112 ◽  
Author(s):  
John Bamberg
Keyword(s):  
Permutation Groups ◽  
Primitive Groups ◽  
Transitive Groups ◽  
Parameter Bounds

AbstractFinite innately transitive permutation groups include all finite quasiprimitive and primitive permutation groups. In this paper, results in the theory of quasiprimitive and primitive groups are generalised to innately transitive groups, and in particular, we extend results of Praeger and Shalev. Thus we show that innately transitive groups possess parameter bounds which are similar to those for primitive groups. We also classify the innately transitive types of quotient actions of innately transitive groups.

Research on Consolidation Modal of Sand-Drained Layer Ground with Impeded Boundaries under Hierarchical Loadings

2014 ◽  
Vol 584-586 ◽  
pp. 2068-2076
Author(s):  
Hong Xing Zhou ◽  
Yong Cha Lin ◽  
Zhi Liang Dong ◽  
Ping Shan Chen
Keyword(s):  
Measured Data ◽  
Computational Results ◽  
Sand Layer ◽  
Research Results ◽  
The Difference ◽  
Cushion Layer ◽  
Consolidation Analysis ◽  
The Ideal

In practical, the drainage cushion layer (such as sand layer) has certain permeability. It means the permeability of the drainage cushion layer is neither a infinitesimal or infinity. This condition is named as the semi-permeable boundary. In the existing consolidation analysis, this condition is simplified as the ideal drainage boundaries. And the difference between the computational results and measured data is big. Based on the existing research results, the consolidation modal of sand-drained layer ground with the impeded boundaries under hierarchical loadings is derived. The compared results show the modal is reasonable.

The Mathieu Groups

1951 ◽  
Vol 3 ◽  
pp. 164-174 ◽  
Author(s):  
R. G. Stanton
Keyword(s):  
Simple Groups ◽  
Permutation Groups ◽  
Alternating Groups ◽  
Mathieu Groups ◽  
In Virtue Of

An enumeration of known simple groups has been given by Dickson [17]; to this list, he made certain additions in later papers [15], [16]. However, with but five exceptions, all known simple groups fall into infinite families; these five unusual simple groups were discovered by Mathieu [21], [22] and, after occasioning some discussion [20], [23], [27], were relegated to the position, which they still hold, of freakish groups without known relatives. Further interest is attached to these Mathieu groups in virtue of their providing the only known examples (other than the trivial examples of the symmetric and alternating groups) of quadruply and quintuply transitive permutation groups.

scholarly journals A Note on Primitive Permutation Groups of Prime Power Degree

2015 ◽  
Vol 2015 ◽  
pp. 1-4
Author(s):  
Qian Cai ◽  
Hua Zhang
Keyword(s):  
Prime Power ◽  
Permutation Groups ◽  
Simple Type ◽  
Present Stage ◽  
Primitive Groups ◽  
Short Survey ◽  
Product Action ◽  
Action Type ◽  
Affine Type

Primitive permutation groups of prime power degree are known to be affine type, almost simple type, and product action type. At the present stage finding an explicit classification of primitive groups of affine type seems untractable, while the product action type can usually be reduced to almost simple type. In this paper, we present a short survey of the development of primitive groups of prime power degree, together with a brief description on such groups.

Supplements of bounded permutation groups

1998 ◽  
Vol 63 (1) ◽  
pp. 89-102 ◽  
Author(s):  
Stephen Bigelow
Keyword(s):  
Symmetric Group ◽  
Permutation Group ◽  
Permutation Groups ◽  
Cardinal Arithmetic

AbstractLet λ ≤ κ be infinite cardinals and let Ω be a set of cardinality κ. The bounded permutation group Bλ(Ω), or simply Bλ, is the group consisting of all permutations of Ω which move fewer than λ points in Ω. We say that a permutation group G acting on Ω is a supplement of Bλ if BλG is the full symmetric group on Ω.In [7], Macpherson and Neumann claimed to have classified all supplements of bounded permutation groups. Specifically, they claimed to have proved that a group G acting on the set Ω is a supplement of Bλ if and only if there exists Δ ⊂ Ω with ∣Δ∣ < λ such that the setwise stabiliser G{Δ} acts as the full symmetric group on Ω ∖ Δ. However I have found a mistake in their proof. The aim of this paper is to examine conditions under which Macpherson and Neumann's claim holds, as well as conditions under which a counterexample can be constructed. In the process we will discover surprising links with cardinal arithmetic and Shelah's recently developed pcf theory.

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