An elementary abelian group of large rank is not a CI-group

M. Muzychuk

doi:10.1016/S0012-365X(02)00558-7

An elementary abelian group of large rank is not a CI-group

M. Muzychuk

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

Abstract

In this paper, we prove that the group Z _(p) ⁽ⁿ⁾ is not a CI-group if n≥2p-1+( ^2p-1 _p), that is there exist two Cayley digraphs over Z(p)(n) which are isomorphic but their connection sets are not conjugate by an automorphism of Z(p)(n).

Original language	English
Pages (from-to)	167-185
Number of pages	19
Journal	Discrete Mathematics
Volume	264
Issue number	1-3
DOIs	https://doi.org/10.1016/S0012-365X(02)00558-7
State	Published - 6 Mar 2003
Externally published	Yes

Keywords

CI-group
Cayley graphs
Schur rings

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/S0012-365X(02)00558-7

Cite this

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title = "An elementary abelian group of large rank is not a CI-group",

abstract = "In this paper, we prove that the group Z (p) (n) is not a CI-group if n≥2p-1+( 2p-1 p), that is there exist two Cayley digraphs over Z(p)(n) which are isomorphic but their connection sets are not conjugate by an automorphism of Z(p)(n).",

keywords = "CI-group, Cayley graphs, Schur rings",

author = "M. Muzychuk",

note = "Funding Information: Partially supported by the Israeli Ministry of Absorption.",

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AU - Muzychuk, M.

N1 - Funding Information: Partially supported by the Israeli Ministry of Absorption.

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Y1 - 2003/3/6

N2 - In this paper, we prove that the group Z (p) (n) is not a CI-group if n≥2p-1+( 2p-1 p), that is there exist two Cayley digraphs over Z(p)(n) which are isomorphic but their connection sets are not conjugate by an automorphism of Z(p)(n).

AB - In this paper, we prove that the group Z (p) (n) is not a CI-group if n≥2p-1+( 2p-1 p), that is there exist two Cayley digraphs over Z(p)(n) which are isomorphic but their connection sets are not conjugate by an automorphism of Z(p)(n).

KW - CI-group

KW - Cayley graphs

KW - Schur rings

UR - https://www.scopus.com/pages/publications/84867969451

U2 - 10.1016/S0012-365X(02)00558-7

DO - 10.1016/S0012-365X(02)00558-7

M3 - Article

AN - SCOPUS:84867969451

SN - 0012-365X

VL - 264

SP - 167

EP - 185

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -

An elementary abelian group of large rank is not a CI-group

Abstract

Keywords

ASJC Scopus subject areas

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