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

Katedra Matematyki (RMS/RMS1)

Silesian University of Technology

Wyniki badań: Wkład do czasopisma › Artykuł › recenzja

1 Cytowanie z bazy Scopus

Abstrakt

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.

Język oryginału	angielski
Strony (od–do)	306-312
Liczba stron	7
Czasopismo	Journal of Algebra
Tom	341
Numer wydania	1
Identyfikatory DOI	https://doi.org/10.1016/j.jalgebra.2011.06.025
Status publikacji	Opublikowano - 1 wrz 2011

Obszary tematyczne ASJC Scopus

Algebra i teoria liczb

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10.1016/j.jalgebra.2011.06.025

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Cytowanie

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author = "Zbigniew Szaszkowski and Witold Tomaszewski",

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AU - Tomaszewski, Witold

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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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DO - 10.1016/j.jalgebra.2011.06.025

M3 - Article

AN - SCOPUS:79960582886

SN - 0021-8693

VL - 341

SP - 306

EP - 312

JO - Journal of Algebra

JF - Journal of Algebra

IS - 1

ER -

On mep-relations in the wreath product of groups

Abstrakt

Obszary tematyczne ASJC Scopus

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