The class-breadth conjecture revisited
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Eick, Bettina; Newman, Michael; O'Brien, E A
Description
The class-breadth conjecture for groups with prime-power order was formulated by Leedham-Green, Neumann and Wiegold in 1969. We construct a new counter-example to the conjecture: it has order 219 and is a quotient of a 4-dimensional 2-uniserial space group. We translate the conjecture to p-uniserial space groups, prove that these have finite cobreadth, and provide an explicit upper bound. We develop an algorithm to decide the conjecture for p-uniserial space groups, and use this to show that...[Show more]
dc.contributor.author | Eick, Bettina | |
---|---|---|
dc.contributor.author | Newman, Michael | |
dc.contributor.author | O'Brien, E A | |
dc.date.accessioned | 2015-12-07T22:53:39Z | |
dc.identifier.issn | 0021-8693 | |
dc.identifier.uri | http://hdl.handle.net/1885/27828 | |
dc.description.abstract | The class-breadth conjecture for groups with prime-power order was formulated by Leedham-Green, Neumann and Wiegold in 1969. We construct a new counter-example to the conjecture: it has order 219 and is a quotient of a 4-dimensional 2-uniserial space group. We translate the conjecture to p-uniserial space groups, prove that these have finite cobreadth, and provide an explicit upper bound. We develop an algorithm to decide the conjecture for p-uniserial space groups, and use this to show that all 3-uniserial space groups of dimension at most 54 satisfy the conjecture. We show that over every finite field there are Lie algebras which fail the corresponding conjecture. | |
dc.publisher | Elsevier | |
dc.source | Journal of Algebra | |
dc.title | The class-breadth conjecture revisited | |
dc.type | Journal article | |
local.description.notes | Imported from ARIES | |
local.identifier.citationvolume | 300 | |
dc.date.issued | 2006 | |
local.identifier.absfor | 010105 - Group Theory and Generalisations | |
local.identifier.ariespublication | u3488905xPUB54 | |
local.type.status | Published Version | |
local.contributor.affiliation | Eick, Bettina, University of Braunschweig | |
local.contributor.affiliation | Newman, Michael, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | O'Brien, E A, University of Auckland | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.startpage | 384 | |
local.bibliographicCitation.lastpage | 393 | |
local.identifier.doi | 10.1016/j.jalgebra.2006.03.010 | |
dc.date.updated | 2015-12-07T12:41:24Z | |
local.identifier.scopusID | 2-s2.0-33646572894 | |
Collections | ANU Research Publications |
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