On Schur p-Groups of odd order › Research Explorer

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On Schur p-Groups of odd order. / Ryabov, Grigory.

In: Journal of Algebra and its Applications, Vol. 16, No. 3, 1750045, 01.03.2017.

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

Harvard

Ryabov, G 2017, 'On Schur p-Groups of odd order', Journal of Algebra and its Applications, vol. 16, no. 3, 1750045. https://doi.org/10.1142/S0219498817500451

APA

Ryabov, G. (2017). On Schur p-Groups of odd order. Journal of Algebra and its Applications, 16(3), [1750045]. https://doi.org/10.1142/S0219498817500451

Vancouver

Ryabov G. On Schur p-Groups of odd order. Journal of Algebra and its Applications. 2017 Mar 1;16(3):1750045. doi: 10.1142/S0219498817500451

Author

Ryabov, Grigory. / On Schur p-Groups of odd order. In: Journal of Algebra and its Applications. 2017 ; Vol. 16, No. 3.

BibTeX

@article{43f9ad6da3294457acf376cf70f69b86,

title = "On Schur p-Groups of odd order",

abstract = "A finite group G is called a Schur group if any S-ring over G is associated in a natural way with a subgroup of Sym(G) that contains all right translations. We prove that the groups Z3 × Z3n, where n ≥ 1, are Schur. Modulo previously obtained results, it follows that every noncyclic Schur p-group, where p is an odd prime, is isomorphic to Z3 × Z3 × Z3 or Z3 × Z3n, n ≥ 1.",

keywords = "Cayley schemes, Permutation groups, S -rings, Schur groups, Srings",

author = "Grigory Ryabov",

note = "Publisher Copyright: {\textcopyright} 2017 World Scientific Publishing Company.",

year = "2017",

month = mar,

day = "1",

doi = "10.1142/S0219498817500451",

language = "English",

volume = "16",

journal = "Journal of Algebra and its Applications",

issn = "0219-4988",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "3",

}

RIS

TY - JOUR

T1 - On Schur p-Groups of odd order

AU - Ryabov, Grigory

PY - 2017/3/1

Y1 - 2017/3/1

N2 - A finite group G is called a Schur group if any S-ring over G is associated in a natural way with a subgroup of Sym(G) that contains all right translations. We prove that the groups Z3 × Z3n, where n ≥ 1, are Schur. Modulo previously obtained results, it follows that every noncyclic Schur p-group, where p is an odd prime, is isomorphic to Z3 × Z3 × Z3 or Z3 × Z3n, n ≥ 1.

AB - A finite group G is called a Schur group if any S-ring over G is associated in a natural way with a subgroup of Sym(G) that contains all right translations. We prove that the groups Z3 × Z3n, where n ≥ 1, are Schur. Modulo previously obtained results, it follows that every noncyclic Schur p-group, where p is an odd prime, is isomorphic to Z3 × Z3 × Z3 or Z3 × Z3n, n ≥ 1.

KW - Cayley schemes

KW - Permutation groups

KW - S -rings

KW - Schur groups

KW - Srings

UR - http://www.scopus.com/inward/record.url?scp=84962719367&partnerID=8YFLogxK

U2 - 10.1142/S0219498817500451

DO - 10.1142/S0219498817500451

M3 - Article

AN - SCOPUS:84962719367

VL - 16

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

SN - 0219-4988

IS - 3

M1 - 1750045

ER -

ID: 9030005