Abelian Schur groups of odd order

Ilia Nikolaevich Ponomarenko; Grigory Konstantinovich Ryabov

Abelian Schur groups of odd order

Ilia Nikolaevich Ponomarenko, Grigory Konstantinovich Ryabov

Higher Mathematics Section

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

1 Citation (Scopus)

Abstract

A finite group G is called a Schur group if any Schur ring over G is associated in a natural way with a subgroup of Sym(G) that contains all right translations. It is proved that the group C₃ × C₃ × C_p is Schur for any prime p. Together with earlier results, this completes a classification of the abelian Schur groups of odd order.

Original language	English
Pages (from-to)	397-411
Number of pages	15
Journal	Сибирские электронные математические известия
Volume	15
Publication status	Published - 1 Jan 2018

Keywords

Permutation groups
Schur groups
Schur rings

OECD FOS+WOS

1.01 MATHEMATICS

Cite this

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abstract = "A finite group G is called a Schur group if any Schur ring over G is associated in a natural way with a subgroup of Sym(G) that contains all right translations. It is proved that the group C3 × C3 × Cp is Schur for any prime p. Together with earlier results, this completes a classification of the abelian Schur groups of odd order.",

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AU - Ponomarenko, Ilia Nikolaevich

AU - Ryabov, Grigory Konstantinovich

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N2 - A finite group G is called a Schur group if any Schur ring over G is associated in a natural way with a subgroup of Sym(G) that contains all right translations. It is proved that the group C3 × C3 × Cp is Schur for any prime p. Together with earlier results, this completes a classification of the abelian Schur groups of odd order.

AB - A finite group G is called a Schur group if any Schur ring over G is associated in a natural way with a subgroup of Sym(G) that contains all right translations. It is proved that the group C3 × C3 × Cp is Schur for any prime p. Together with earlier results, this completes a classification of the abelian Schur groups of odd order.

KW - Permutation groups

KW - Schur groups

KW - Schur rings

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AN - SCOPUS:85058230424

VL - 15

SP - 397

EP - 411

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

Abelian Schur groups of odd order

Abstract

Keywords

OECD FOS+WOS

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