• On sets of elements of the sam...

Treffer: On sets of elements of the same order in the alternating group $A_n$: On sets of elements of the same order in the alternating group \(A_n\)

Title:
On sets of elements of the same order in the alternating group $A_n$: On sets of elements of the same order in the alternating group \(A_n\)
Authors:
Bagiński, Czesław
Source:
Publicationes Mathematicae Debrecen. 34:313-315
Publisher Information:
University of Debrecen/ Debreceni Egyetem, 2022.
Publication Year:
2022
Subject Terms:
Subgroups of symmetric groups, Generators, relations, and presentations of groups, 0101 mathematics, 01 natural sciences, Arithmetic and combinatorial problems involving abstract finite groups, products of elements of order 2, products of elements of order 3
Document Type:
Fachzeitschrift Article
File Description:
application/xml
ISSN:
0033-3883
DOI:
10.5486/pmd.1987.34.3-4.15
Access URL:
https://zbmath.org/4093729
Accession Number:
edsair.doi.dedup.....93c8c4f5285245cc977b8bdec48aa95e
Database:
OpenAIRE

Weitere Informationen

In the paper under review the following theorems are proved. Theorem A: For \(n>4\), every element of \(A_ n\) can be written as the product of two elements of order 2 in \(A_ n\) if and only if \(n\in \{5,6,10,14\}\). Theorem B: For \(n>2\), every element of \(A_ n\) is the product of two elements of order 3. Theorem A is a strengthening of a result of \textit{J. L. Brenner}, \textit{M. Randall} and \textit{J. Riddell} [Colloq. Math. 32, 39-48 (1974; Zbl 0273.20003)]. Theorem B is a rediscovery of a result of \textit{J. L. Brenner} and \textit{J. Riddell} [Am. Math. Mon. 84, 39-40 (1977; Zbl 0445.05002)]. \textit{J. L. Brenner} and \textit{R. J. Evans} [J. Comb. Theory, Ser. A 45, 196-206 (1987; Zbl 0621.20017)] proved the corresponding result for elements of order 5 if \(n\geq 15\).