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The Size of a Minimal Generating Set for Primitive3/2 -Transitive Groups. / Vasil’ev, A. V.; Zvezdina, M. A.; Churikov, D. V.

In: Siberian Mathematical Journal, Vol. 63, No. 6, 11.2022, p. 1041-1048.

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

Harvard

Vasil’ev, AV, Zvezdina, MA & Churikov, DV 2022, 'The Size of a Minimal Generating Set for Primitive3/2 -Transitive Groups', Siberian Mathematical Journal, vol. 63, no. 6, pp. 1041-1048. https://doi.org/10.1134/S0037446622060039

APA

Vasil’ev, A. V., Zvezdina, M. A., & Churikov, D. V. (2022). The Size of a Minimal Generating Set for Primitive3/2 -Transitive Groups. Siberian Mathematical Journal, 63(6), 1041-1048. https://doi.org/10.1134/S0037446622060039

Vancouver

Vasil’ev AV, Zvezdina MA, Churikov DV. The Size of a Minimal Generating Set for Primitive3/2 -Transitive Groups. Siberian Mathematical Journal. 2022 Nov;63(6):1041-1048. doi: 10.1134/S0037446622060039

Author

Vasil’ev, A. V. ; Zvezdina, M. A. ; Churikov, D. V. / The Size of a Minimal Generating Set for Primitive3/2 -Transitive Groups. In: Siberian Mathematical Journal. 2022 ; Vol. 63, No. 6. pp. 1041-1048.

BibTeX

@article{2f2e0e7d37154331804e9f9491d3f612,
title = "The Size of a Minimal Generating Set for Primitive3/2 -Transitive Groups",
abstract = "We refer to d(G) as the minimal size of a generating set ofa finite group G, and say that G is d -generated if d(G)≤ d.A transitive permutation group G is called 3/2-transitive ifthe point stabilizer Gαis nontrivial and its orbits distinct from α are of the same size.We prove that d(G)≤ 4 for every primitive 3/2-transitive permutation group G and, moreover,G is 2-generated except for the rather particular solvable affine groupsthat we describe completely.In particular, all finite 2-transitive and 2-homogeneous groups are 2-generated.We also show that every finite group whose abelian subgroups are cyclic is 2-generated,and so is every Frobenius complement.",
keywords = "2-homogeneous group, 2-transitive group, 3/2-transitive group, Frobenius complement, minimal generating set, primitive permutation group",
author = "Vasil{\textquoteright}ev, {A. V.} and Zvezdina, {M. A.} and Churikov, {D. V.}",
note = "Funding Information: The authors were supported by the Ministry of Science and Higher Education of the Russian Federation (Project FWNF–2022–0002). Publisher Copyright: {\textcopyright} 2022, Pleiades Publishing, Ltd.",
year = "2022",
month = nov,
doi = "10.1134/S0037446622060039",
language = "English",
volume = "63",
pages = "1041--1048",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",
number = "6",

}

RIS

TY - JOUR

T1 - The Size of a Minimal Generating Set for Primitive3/2 -Transitive Groups

AU - Vasil’ev, A. V.

AU - Zvezdina, M. A.

AU - Churikov, D. V.

N1 - Funding Information: The authors were supported by the Ministry of Science and Higher Education of the Russian Federation (Project FWNF–2022–0002). Publisher Copyright: © 2022, Pleiades Publishing, Ltd.

PY - 2022/11

Y1 - 2022/11

N2 - We refer to d(G) as the minimal size of a generating set ofa finite group G, and say that G is d -generated if d(G)≤ d.A transitive permutation group G is called 3/2-transitive ifthe point stabilizer Gαis nontrivial and its orbits distinct from α are of the same size.We prove that d(G)≤ 4 for every primitive 3/2-transitive permutation group G and, moreover,G is 2-generated except for the rather particular solvable affine groupsthat we describe completely.In particular, all finite 2-transitive and 2-homogeneous groups are 2-generated.We also show that every finite group whose abelian subgroups are cyclic is 2-generated,and so is every Frobenius complement.

AB - We refer to d(G) as the minimal size of a generating set ofa finite group G, and say that G is d -generated if d(G)≤ d.A transitive permutation group G is called 3/2-transitive ifthe point stabilizer Gαis nontrivial and its orbits distinct from α are of the same size.We prove that d(G)≤ 4 for every primitive 3/2-transitive permutation group G and, moreover,G is 2-generated except for the rather particular solvable affine groupsthat we describe completely.In particular, all finite 2-transitive and 2-homogeneous groups are 2-generated.We also show that every finite group whose abelian subgroups are cyclic is 2-generated,and so is every Frobenius complement.

KW - 2-homogeneous group

KW - 2-transitive group

KW - 3/2-transitive group

KW - Frobenius complement

KW - minimal generating set

KW - primitive permutation group

UR - http://www.scopus.com/inward/record.url?scp=85143590953&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/77b7f26d-7c36-35f6-9d2f-cd7e14d82f2c/

U2 - 10.1134/S0037446622060039

DO - 10.1134/S0037446622060039

M3 - Article

AN - SCOPUS:85143590953

VL - 63

SP - 1041

EP - 1048

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 6

ER -

ID: 40814233