ON CI-PROPERTY OF THE GROUP \mathbb{Z}_{p}\times \mathbb{Z}_{q}\times \mathbb{Z}_{r}

2018 ◽  
Vol 109 (1) ◽  
pp. 105-115
Author(s):  
Mohamed Soueycatt ◽  
Eskander Ali ◽  
Ahed Hassoon
Keyword(s):  
Ci Property

Isomorphism Problem for Metacirculant Graphs of Order a Product of Distinct Primes

1998 ◽  
Vol 50 (6) ◽  
pp. 1176-1188 ◽  
Author(s):  
Edward Dobson
Keyword(s):  
Cayley Graphs ◽  
Isomorphism Problem ◽  
Circulant Graphs ◽  
Isomorphism Classes ◽  
Simple Characterization ◽  
Vertex Transitive ◽  
Ci Property

AbstractIn this paper, we solve the isomorphism problem for metacirculant graphs of order pq that are not circulant. To solve this problem, we first extend Babai’s characterization of the CI-property to non-Cayley vertex-transitive hypergraphs. Additionally, we find a simple characterization of metacirculant Cayley graphs of order pq, and exactly determine the full isomorphism classes of circulant graphs of order pq.

WEAK PROPER ACTIONS ON SOLVABLE HOMOGENEOUS SPACES

2007 ◽  
Vol 18 (08) ◽  
pp. 903-918 ◽  
Author(s):  
ALI BAKLOUTI ◽  
FATMA KHLIF
Keyword(s):  
Homogeneous Space ◽  
Lie Group ◽  
Homogeneous Spaces ◽  
Proper Action ◽  
Proper Actions ◽  
Simply Connected ◽  
Ci Property ◽  
Solvable Lie Group

Let H and K be closed connected subgroups of a connected, simply connected solvable Lie group G. We define the notion of weak and finite proper action of K on the homogeneous space X = G/H and prove that they are equivalent to the notion of (CI)-action of K on X in the sense of Kobayashi. We show also that the action of K on X is proper if and only if the solvable triple (G, H, K) has the (CI) property in both cases where one of those subgroups is maximal and where G is special.

scholarly journals CI-Property for Decomposable Schur Rings over an Abelian Group

2019 ◽  
Vol 26 (01) ◽  
pp. 147-160 ◽  
Author(s):  
István Kovács ◽  
Grigory Ryabov
Keyword(s):  
Finite Group ◽  
Abelian Group ◽  
Wreath Product ◽  
Direct Product ◽  
Elementary Abelian Group ◽  
Sufficient Condition ◽  
Schur Ring ◽  
Generalized Wreath Product ◽  
A Finite Group ◽  
Ci Property

A Schur ring over a finite group is said to be decomposable if it is the generalized wreath product of Schur rings over smaller groups. In this paper we establish a sufficient condition for a decomposable Schur ring over the direct product of elementary abelian groups to be a CI-Schur ring. By using this condition we offer short proofs for some known results on the CI-property for decomposable Schur rings over an elementary abelian group of rank at most 5.

scholarly journals On finite groups with the Cayley invariant property

1997 ◽  
Vol 56 (2) ◽  
pp. 253-261
Author(s):  
Cai Heng Li
Keyword(s):  
Finite Group ◽  
Simple Group ◽  
Finite Groups ◽  
Cayley Graphs ◽  
Invariant Property ◽  
Frobenius Groups ◽  
Nonabelian Simple Group ◽  
A Finite Group ◽  
Ci Property

A finite group G is said to have the m-CI property if, for any two Cayley graphs Cay(G, S) and Cay(G, T) of valency m, Cay(G, S) ≅ Cay(G, T) implies Sσ = T for some automorphism σ of G. In this paper, we investigate finite groups with the m-CI property. We first construct groups with the 3-CI property but not with the 2-CI property, and then prove that a nonabelian simple group has the 3-CI property if and only if it is A5. Finally, for infinitely many values of m, we construct Frobenius groups with the m-CI property but not with the nontrivial k-CI property for any k < m.

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