The action of sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their cayley graphs

Bartłomiej Pawlik

The action of sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their cayley graphs

Bartłomiej Pawlik

Department of Mathematics (RMS/RMS1)

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

4 Citations (Scopus)

Abstract

Base (minimal generating set) of the Sylow 2-subgroup of (formula presented) is called diagonal if every element of this set acts non-trivially only on one coordinate, and different elements act on different coordinates. The Sylow 2-subgroup P_n(2) of (formula presented) acts by conjugation on the set of all bases. In presented paper the stabilizer of the set of all diagonal bases in S_n(2) is characterized and the orbits of the action are determined. It is shown that every orbit contains exactly 2ⁿ⁻¹ diagonal bases and (formula presented) bases at all. Recursive construction of Cayley graphs of P_n(2) on diagonal bases (n ≥ 2) is proposed.

Original language	English
Pages (from-to)	264-281
Number of pages	18
Journal	Algebra and Discrete Mathematics
Volume	21
Issue number	2
Publication status	Published - 2016

Keywords

Cayley graphs
Group base
Sylow p-subgroup
Wreath product of groups

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

Cite this

@article{1a0d4e92265b47c0b840aedf890d77e0,

title = "The action of sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their cayley graphs",

abstract = "Base (minimal generating set) of the Sylow 2-subgroup of (formula presented) is called diagonal if every element of this set acts non-trivially only on one coordinate, and different elements act on different coordinates. The Sylow 2-subgroup Pn(2) of (formula presented) acts by conjugation on the set of all bases. In presented paper the stabilizer of the set of all diagonal bases in Sn(2) is characterized and the orbits of the action are determined. It is shown that every orbit contains exactly 2n−1 diagonal bases and (formula presented) bases at all. Recursive construction of Cayley graphs of Pn(2) on diagonal bases (n ≥ 2) is proposed.",

keywords = "Cayley graphs, Group base, Sylow p-subgroup, Wreath product of groups",

author = "Bart{\l}omiej Pawlik",

note = "Publisher Copyright: {\textcopyright} Journal “Algebra and Discrete Mathematics”.",

year = "2016",

language = "English",

volume = "21",

pages = "264--281",

journal = "Algebra and Discrete Mathematics",

issn = "1726-3255",

publisher = "Lugansk Taras Shevchenko National University",

number = "2",

}

TY - JOUR

T1 - The action of sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their cayley graphs

AU - Pawlik, Bartłomiej

N1 - Publisher Copyright: © Journal “Algebra and Discrete Mathematics”.

PY - 2016

Y1 - 2016

N2 - Base (minimal generating set) of the Sylow 2-subgroup of (formula presented) is called diagonal if every element of this set acts non-trivially only on one coordinate, and different elements act on different coordinates. The Sylow 2-subgroup Pn(2) of (formula presented) acts by conjugation on the set of all bases. In presented paper the stabilizer of the set of all diagonal bases in Sn(2) is characterized and the orbits of the action are determined. It is shown that every orbit contains exactly 2n−1 diagonal bases and (formula presented) bases at all. Recursive construction of Cayley graphs of Pn(2) on diagonal bases (n ≥ 2) is proposed.

AB - Base (minimal generating set) of the Sylow 2-subgroup of (formula presented) is called diagonal if every element of this set acts non-trivially only on one coordinate, and different elements act on different coordinates. The Sylow 2-subgroup Pn(2) of (formula presented) acts by conjugation on the set of all bases. In presented paper the stabilizer of the set of all diagonal bases in Sn(2) is characterized and the orbits of the action are determined. It is shown that every orbit contains exactly 2n−1 diagonal bases and (formula presented) bases at all. Recursive construction of Cayley graphs of Pn(2) on diagonal bases (n ≥ 2) is proposed.

KW - Cayley graphs

KW - Group base

KW - Sylow p-subgroup

KW - Wreath product of groups

UR - https://www.scopus.com/pages/publications/84978042670

M3 - Article

AN - SCOPUS:84978042670

SN - 1726-3255

VL - 21

SP - 264

EP - 281

JO - Algebra and Discrete Mathematics

JF - Algebra and Discrete Mathematics

IS - 2

ER -

The action of sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their cayley graphs

Abstract

Keywords

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this