dc.contributor.author | Mahmood, Shuker | |
dc.contributor.author | Rajah, Andrew | |
dc.date.accessioned | 2018-07-26T05:56:06Z | |
dc.date.available | 2018-07-26T05:56:06Z | |
dc.date.issued | 2011 | |
dc.identifier.issn | 1815-3852 | |
dc.identifier.uri | https://journal.uob.edu.bh:443/handle/123456789/856 | |
dc.description.abstract | In this paper we find the solutions to the class equation xd = β in the alternating group An (i.e. find the solutions set X = {x ∈ An∣xd ∈ A(β)}) and find the number of these solutions ∣X∣ for each β ∈ H ∩ Cα and n ∉ θ, where H = {Cα of Sn∣n > 1, with all parts αk of α different and odd}. Cα is a conjugacy class of Sn and forms classes, where Cα depends on the cycle partition α of its elements. If (14 > n ∉ θ ∪ {9, 11, 13}) and β ∈ H ∩ Cα in An, then Fn contains Cα, where Fn = {Cα of Sn∣ the number of parts αk of α with the property αk ≡ 3 (mod 4) is odd}. In this work we introduce several theorems to solve the class equation xd = β in the alternating group An where β ∈ H ∩ Cα and n ∉ θ and we find the number of the solutions for n to be: (i) 14 > n ∉ θ, (ii) 14 > n ∉ θ and (n + 1) ∉ θ, (iii) 14 > n ∉ θ and Cα ≠ [1, 3, 7], (iv) n = 9, 11, 13, (v) n > 14. | en_US |
dc.language.iso | en | en_US |
dc.publisher | University of Bahrain | en_US |
dc.rights | Attribution-NonCommercial-ShareAlike 4.0 International | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-sa/4.0/ | * |
dc.subject | Alternating groups | |
dc.subject | Permutations | |
dc.subject | Conjugate classes | |
dc.subject | Cycle type | |
dc.subject | Ambivalent groups | |
dc.title | Solving the class equation xd = β in an alternating group for each β ∈ H ∩ Cα and n ∉ θ | en_US |
dc.type | Article | en_US |
dc.identifier.doi | http://dx.doi.org/10.1016/j.jaubas.2011.06.006 | |
dc.source.title | Arab Journal of Basic and Applied Sciences | |
dc.abbreviatedsourcetitle | AJBAS |