The Cayley isomorphism property for p 3 × q
Algebraic Combinatorics, Volume 4 (2021) no. 2, pp. 289-299.

For every pair of distinct primes p, q, where q>2 we prove that p 3 × q is a CI-group with respect to binary relational structures.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.154
Classification: 05C25, 05C60, 20B25
Keywords: Cayley graphs, CI property.

Somlai, Gábor 1; Muzychuk, Mikhail 2

1 Eötvös Loránd University Departement of Algebra and Number Theory Pázmány Péter sétány 1/c Budapest 1117, Hungary
2 Ben Gurion University of the Negev, Israël
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
@article{ALCO_2021__4_2_289_0,
     author = {Somlai, G\'abor and Muzychuk, Mikhail},
     title = {The {Cayley} isomorphism property for $\protect \mathbb{Z}_{p}^{3} \times \protect \mathbb{Z}_{q}$},
     journal = {Algebraic Combinatorics},
     pages = {289--299},
     publisher = {MathOA foundation},
     volume = {4},
     number = {2},
     year = {2021},
     doi = {10.5802/alco.154},
     language = {en},
     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.154/}
}
TY  - JOUR
AU  - Somlai, Gábor
AU  - Muzychuk, Mikhail
TI  - The Cayley isomorphism property for $\protect \mathbb{Z}_{p}^{3} \times \protect \mathbb{Z}_{q}$
JO  - Algebraic Combinatorics
PY  - 2021
SP  - 289
EP  - 299
VL  - 4
IS  - 2
PB  - MathOA foundation
UR  - https://alco.centre-mersenne.org/articles/10.5802/alco.154/
DO  - 10.5802/alco.154
LA  - en
ID  - ALCO_2021__4_2_289_0
ER  - 
%0 Journal Article
%A Somlai, Gábor
%A Muzychuk, Mikhail
%T The Cayley isomorphism property for $\protect \mathbb{Z}_{p}^{3} \times \protect \mathbb{Z}_{q}$
%J Algebraic Combinatorics
%D 2021
%P 289-299
%V 4
%N 2
%I MathOA foundation
%U https://alco.centre-mersenne.org/articles/10.5802/alco.154/
%R 10.5802/alco.154
%G en
%F ALCO_2021__4_2_289_0
Somlai, Gábor; Muzychuk, Mikhail. The Cayley isomorphism property for $\protect \mathbb{Z}_{p}^{3} \times \protect \mathbb{Z}_{q}$. Algebraic Combinatorics, Volume 4 (2021) no. 2, pp. 289-299. doi : 10.5802/alco.154. https://alco.centre-mersenne.org/articles/10.5802/alco.154/

[1] Ádám, András Research problem 2-10, Journal of Combinatorial Theory, Volume 2 (1967) no. 3, p. 393 | DOI

[2] Alspach, Brian; Parsons, Torrence D. Isomorphism of circulant graphs and digraphs, Discrete Math., Volume 25 (1979) no. 2, pp. 97-108 | DOI | MR | Zbl

[3] Babai, László Isomorphism problem for a class of point-symmetric structures, Acta Math. Acad. Sci. Hungar., Volume 29 (1977) no. 3-4, pp. 329-336 | DOI | MR | Zbl

[4] Babai, László; Frankl, Péter Isomorphisms of Cayley graphs. I, Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. I (Colloq. Math. Soc. János Bolyai), Volume 18 (1978), pp. 35-52 | MR | Zbl

[5] Djoković, Dragomir Ž. Isomorphism problem for a special class of graphs, Acta Math. Acad. Sci. Hungar., Volume 21 (1970) no. 3-4, pp. 267-270 | DOI | MR

[6] Dobson, Edward The isomorphism problem for Cayley ternary relational structures for some abelian groups of order 8p, Discrete Math., Volume 310 (2010) no. 21, pp. 2895-2909 | DOI | MR | Zbl

[7] Dobson, Ted Some new groups which are not CI-groups with respect to graphs, Electron. J. Combin., Volume 25 (2018) no. 1, Paper no. 1.12, 7 pages | MR | Zbl

[8] Elspas, Bernard; Turner, James Graphs with circulant adjacency matrices, J. Combinatorial Theory, Volume 9 (1970), pp. 297-307 | DOI | MR | Zbl

[9] Evdokimov, Sergei A.; Ponomarenko, Ilya N. Schurity of S-rings over a cyclic group and generalized wreath product of permutation groups, St. Petersbg. Math. J., Volume 24 (2013) no. 3, pp. 431-460 | DOI | MR | Zbl

[10] Feng, Yan-Quan; Kovács, István Elementary abelian groups of rank 5 are DCI-groups, J. Combin. Theory Ser. A, Volume 157 (2018), pp. 162-204 | DOI | MR | Zbl

[11] Godsil, Christopher D. On Cayley graph isomorphisms, Ars Comb., Volume 15 (1983), pp. 231-246

[12] Hirasaka, Mitsugu; Muzychuk, Mikhail An elementary abelian group of rank 4 is a CI-group, J. Combin. Theory Ser. A, Volume 94 (2001) no. 2, pp. 339-362 | DOI | MR | Zbl

[13] Klin, Mikhail H.; Pöschel, Reinhard The König problem, the isomorphism problem for cyclic graphs and the method of Schur rings, Algebraic methods in graph theory, Vol. I, II (Szeged, 1978) (Colloq. Math. Soc. János Bolyai), Volume 25, North-Holland, Amsterdam-New York, 1981, pp. 405-434 | MR

[14] Kovács, István; Muzychuk, Mikhail The group p 2 × q is a CI-group, Comm. Algebra, Volume 37 (2009) no. 10, pp. 3500-3515 | DOI | MR

[15] Kovács, István; Ryabov, Grigory CI-property for decomposable Schur rings over an abelian group, Algebra Colloq., Volume 26 (2019) no. 1, pp. 147-160 | DOI | MR | Zbl

[16] Li, Cai Heng; Lu, Zai Ping; Pálfy, PP Further restrictions on the structure of finite CI-groups, J. Algebraic Combin., Volume 26 (2007) no. 2, pp. 161-181 | DOI | MR | Zbl

[17] Morris, Joy Elementary proof that p 4 is a DCI-group, Discrete Math., Volume 338 (2015) no. 8, pp. 1385-1393 | DOI | MR | Zbl

[18] Muzychuk, Mikhail Ádám’s conjecture is true in the square-free case, J. Combin. Theory Ser. A, Volume 72 (1995) no. 1, pp. 118-134 | DOI | MR | Zbl

[19] Muzychuk, Mikhail On Ádám’s conjecture for circulant graphs, Discrete Math., Volume 167/168 (1997), pp. 497-510 | DOI | MR | Zbl

[20] Pöschel, Reinhard Untersuchungen von S-Ringen, insbesondere im Gruppenring von p-Gruppen, Math. Nachr., Volume 60 (1974), pp. 1-27 | DOI | MR | Zbl

[21] Schur, Issai Zur Theorie der einfach transitiven Permutationsgruppen, 1933, Preußische Akademie der Wissenschaften, Berlin, 1933, pp. 598-623 | Zbl

[22] Somlai, Gábor Elementary abelian p-groups of rank 2p+3 are not CI-groups, J. Algebraic Combin., Volume 34 (2011) no. 3, pp. 323-335 | DOI | MR | Zbl

[23] Wielandt, Helmut Finite permutation groups, Academic Press, 1964, x+114 pages (reprinted 2014) | MR | Zbl

Cited by Sources: