Generalizations of Brandl's theorem on Engel length

S. G. Quek; K. B. Wong; P. C. Wong

doi:10.1063/1.4801218

Generalizations of Brandl's theorem on Engel length

S. G. Quek, K. B. Wong, P. C. Wong

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other › peer-review

Abstract

Let n < m be positive integers such that [g,_nh]=[g, _mh] and assume that n and m are chosen minimal with respect to this property. Let g_i=[g,_n+ih] where i=1,2,...,m-n. Then π(g,h)=(g₁,...,g_m-n) is called the Engel cycle generated by g and h. The length of the Engel cycle is m-n. A group G is said to have Engel length r, if all the length of the Engel cycles in G divides r. In this paper we discuss the Brandl's theorem on Engel length and give some of its generalizations.

Original language	English
Title of host publication	Proceedings of the 20th National Symposium on Mathematical Sciences, SKSM 2012 - Research in Mathematical Sciences
Subtitle of host publication	A Catalyst for Creativity and Innovation
Pages	864-865
Number of pages	2
DOIs	https://doi.org/10.1063/1.4801218
Publication status	Published - 2013
Externally published	Yes
Event	National Symposium on Mathematical Sciences 2012 - Putrajaya, Malaysia Duration: 18 Dec 2012 → 20 Dec 2012 Conference number: 20th

Publication series

Name	AIP Conference Proceedings
Volume	1522
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	National Symposium on Mathematical Sciences 2012
Abbreviated title	SKSM 2012
Country/Territory	Malaysia
City	Putrajaya
Period	18/12/12 → 20/12/12
Other	Research in Mathematical Sciences: A Catalyst for Creativity and Innovation

Keywords

Engel cycle
Engel length

Access to Document

10.1063/1.4801218

Cite this

@inproceedings{c260e353d41348c4a10042359ecb1e3d,

title = "Generalizations of Brandl's theorem on Engel length",

abstract = "Let n < m be positive integers such that [g,nh]=[g, mh] and assume that n and m are chosen minimal with respect to this property. Let gi=[g,n+ih] where i=1,2,...,m-n. Then π(g,h)=(g1,...,gm-n) is called the Engel cycle generated by g and h. The length of the Engel cycle is m-n. A group G is said to have Engel length r, if all the length of the Engel cycles in G divides r. In this paper we discuss the Brandl's theorem on Engel length and give some of its generalizations.",

keywords = "Engel cycle, Engel length",

author = "Quek, {S. G.} and Wong, {K. B.} and Wong, {P. C.}",

year = "2013",

doi = "10.1063/1.4801218",

language = "English",

isbn = "9780735411500",

series = "AIP Conference Proceedings",

pages = "864--865",

booktitle = "Proceedings of the 20th National Symposium on Mathematical Sciences, SKSM 2012 - Research in Mathematical Sciences",

note = "National Symposium on Mathematical Sciences 2012, SKSM 2012 ; Conference date: 18-12-2012 Through 20-12-2012",

}

Quek, SG, Wong, KB & Wong, PC 2013, Generalizations of Brandl's theorem on Engel length. in Proceedings of the 20th National Symposium on Mathematical Sciences, SKSM 2012 - Research in Mathematical Sciences: A Catalyst for Creativity and Innovation. AIP Conference Proceedings, vol. 1522, pp. 864-865, National Symposium on Mathematical Sciences 2012, Putrajaya, Malaysia, 18/12/12. https://doi.org/10.1063/1.4801218

Generalizations of Brandl's theorem on Engel length. / Quek, S. G.; Wong, K. B.; Wong, P. C.
Proceedings of the 20th National Symposium on Mathematical Sciences, SKSM 2012 - Research in Mathematical Sciences: A Catalyst for Creativity and Innovation. 2013. p. 864-865 (AIP Conference Proceedings; Vol. 1522).

Research output: Chapter in Book/Report/Conference proceeding › Conference Paper › Other › peer-review

TY - GEN

T1 - Generalizations of Brandl's theorem on Engel length

AU - Quek, S. G.

AU - Wong, K. B.

AU - Wong, P. C.

N1 - Conference code: 20th

PY - 2013

Y1 - 2013

N2 - Let n < m be positive integers such that [g,nh]=[g, mh] and assume that n and m are chosen minimal with respect to this property. Let gi=[g,n+ih] where i=1,2,...,m-n. Then π(g,h)=(g1,...,gm-n) is called the Engel cycle generated by g and h. The length of the Engel cycle is m-n. A group G is said to have Engel length r, if all the length of the Engel cycles in G divides r. In this paper we discuss the Brandl's theorem on Engel length and give some of its generalizations.

AB - Let n < m be positive integers such that [g,nh]=[g, mh] and assume that n and m are chosen minimal with respect to this property. Let gi=[g,n+ih] where i=1,2,...,m-n. Then π(g,h)=(g1,...,gm-n) is called the Engel cycle generated by g and h. The length of the Engel cycle is m-n. A group G is said to have Engel length r, if all the length of the Engel cycles in G divides r. In this paper we discuss the Brandl's theorem on Engel length and give some of its generalizations.

KW - Engel cycle

KW - Engel length

UR - http://www.scopus.com/inward/record.url?scp=84876947829&partnerID=8YFLogxK

U2 - 10.1063/1.4801218

DO - 10.1063/1.4801218

M3 - Conference Paper

AN - SCOPUS:84876947829

SN - 9780735411500

T3 - AIP Conference Proceedings

SP - 864

EP - 865

BT - Proceedings of the 20th National Symposium on Mathematical Sciences, SKSM 2012 - Research in Mathematical Sciences

T2 - National Symposium on Mathematical Sciences 2012

Y2 - 18 December 2012 through 20 December 2012

ER -

Generalizations of Brandl's theorem on Engel length

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Cite this