Non-triviality of some one-relator products of three groups

James Howie; Ihechukwu Chinyere

doi:10.1142/S0218196716500223

Non-triviality of some one-relator products of three groups

James Howie
, Ihechukwu Chinyere

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

135 Downloads (Pure)

Abstract

In this paper we study a group G which is the quotient of a free product of three non-trivial groups by the normal closure of a single element. In particular we show that if the relator has length at most eight, then G is non-trivial. In the case where the factors are cyclic, we prove the stronger result that at least one of the factors embeds in G.

Original language	English
Pages (from-to)	533-550
Number of pages	18
Journal	International Journal of Algebra and Computation
Volume	26
Issue number	3
DOIs	https://doi.org/10.1142/S0218196716500223
Publication status	Published - May 2016

Access to Document

10.1142/S0218196716500223

Download pdf
Electronic version of an article published as International Journal of Algebra and Computation, vol. 26, 2016, 533-550 [10.1142/S0218196716500223] ©World Scientific Publishing Company [http://www.worldscientific.com/worldscinet/ijac]
Accepted author manuscript, 365 KBLicence: All Rights Reserved

Cite this

@article{72a0e55403d84d4abe74ff9a5477ca7e,

title = "Non-triviality of some one-relator products of three groups",

abstract = "In this paper we study a group G which is the quotient of a free product of three non-trivial groups by the normal closure of a single element. In particular we show that if the relator has length at most eight, then G is non-trivial. In the case where the factors are cyclic, we prove the stronger result that at least one of the factors embeds in G.",

author = "James Howie and Ihechukwu Chinyere",

year = "2016",

month = may,

doi = "10.1142/S0218196716500223",

language = "English",

volume = "26",

pages = "533--550",

journal = "International Journal of Algebra and Computation",

issn = "0218-1967",

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

number = "3",

}

TY - JOUR

T1 - Non-triviality of some one-relator products of three groups

AU - Howie, James

AU - Chinyere, Ihechukwu

PY - 2016/5

Y1 - 2016/5

N2 - In this paper we study a group G which is the quotient of a free product of three non-trivial groups by the normal closure of a single element. In particular we show that if the relator has length at most eight, then G is non-trivial. In the case where the factors are cyclic, we prove the stronger result that at least one of the factors embeds in G.

AB - In this paper we study a group G which is the quotient of a free product of three non-trivial groups by the normal closure of a single element. In particular we show that if the relator has length at most eight, then G is non-trivial. In the case where the factors are cyclic, we prove the stronger result that at least one of the factors embeds in G.

U2 - 10.1142/S0218196716500223

DO - 10.1142/S0218196716500223

M3 - Article

SN - 0218-1967

VL - 26

SP - 533

EP - 550

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 3

ER -

Non-triviality of some one-relator products of three groups

Abstract

Access to Document

Fingerprint

Cite this