On mep-relations in the wreath product of groups

Zbigniew Szaszkowski; Witold Tomaszewski

doi:10.1016/j.jalgebra.2011.06.025

On mep-relations in the wreath product of groups

Zbigniew Szaszkowski
, Witold Tomaszewski

Department of Mathematics (RMS/RMS1)

Silesian University of Technology

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

1 Citation (Scopus)

Abstract

Let a, b be two long cycles in an alternating group An, satisfying relations a=[a,_kb] and b=[b,_ka]. We show that every pair of elements of the form x=(X,a), y=(Y,b), where the sum of coefficients of X and Y is equal zero, satisfies relations x=[x,_ly], y=[y,_lx] in the wreath product (S_n2{tone, capital}Z_m)′ for m coprime with n and for an l divisible by k. We show also that for n=5,7,13 and for m coprime with n, (S_n2{tone, capital}Z_m)' is generated by such pairs.

Original language	English
Pages (from-to)	306-312
Number of pages	7
Journal	Journal of Algebra
Volume	341
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2011.06.025
Publication status	Published - 1 Sept 2011

Keywords

Generators and relations
Group theory
Permutation groups
Wreath products

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2011.06.025

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N2 - Let a, b be two long cycles in an alternating group An, satisfying relations a=[a,kb] and b=[b,ka]. We show that every pair of elements of the form x=(X,a), y=(Y,b), where the sum of coefficients of X and Y is equal zero, satisfies relations x=[x,ly], y=[y,lx] in the wreath product (Sn2{tone, capital}Zm)′ for m coprime with n and for an l divisible by k. We show also that for n=5,7,13 and for m coprime with n, (Sn2{tone, capital}Zm)' is generated by such pairs.

AB - Let a, b be two long cycles in an alternating group An, satisfying relations a=[a,kb] and b=[b,ka]. We show that every pair of elements of the form x=(X,a), y=(Y,b), where the sum of coefficients of X and Y is equal zero, satisfies relations x=[x,ly], y=[y,lx] in the wreath product (Sn2{tone, capital}Zm)′ for m coprime with n and for an l divisible by k. We show also that for n=5,7,13 and for m coprime with n, (Sn2{tone, capital}Zm)' is generated by such pairs.

KW - Generators and relations

KW - Group theory

KW - Permutation groups

KW - Wreath products

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ER -

On mep-relations in the wreath product of groups

Abstract

Keywords

ASJC Scopus subject areas

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