On counterexamples to the Hughes conjecture.

DOI10.1016/J.JALGEBRA.2009.04.011zbMath1187.20010OpenAlexW2165992057WikidataQ123356416 ScholiaQ123356416MaRDI QIDQ731246

Michael Vaughan-Lee, George Havas

Publication date: 2 October 2009

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://ora.ox.ac.uk/objects/uuid:da0ebbde-a1c6-41fa-9e24-d9a23d8d0316

zbMATH Keywords

finite \(p\)-groupscounterexamplesLie ringsHughes conjecturepower-commutator presentations

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Special subgroups (Frattini, Fitting, etc.) (20D25) Generators, relations, and presentations of groups (20F05) Finite nilpotent groups, (p)-groups (20D15) Software, source code, etc. for problems pertaining to group theory (20-04) Engel conditions (20F45) Associated Lie structures for groups (20F40)

Related Items (4)

Understanding Wall's theorem on dependence of Lie relators in Burnside groups ⋮ p-GROUPS WITH CYCLIC OR GENERALISED QUATERNION HUGHES SUBGROUPS: CLASSIFYING TIDY p-GROUPS ⋮ Groups having all elements off a normal subgroup with prime power order ⋮ The average element order and the number of conjugacy classes of finite groups

Uses Software

• GAP
• Magma

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A nilpotent quotient algorithm for graded Lie rings
• The \(H_p\)-problem and the structure of \(H_p\)-groups
• On the multilinear identities which hold in the Lie ring of a group of prime-power exponent
• Hughes problem for finite \(p\)-groups.
• The Magma algebra system. I: The user language
• On finite \(p\)-groups not satisfying the Hughes conjecture
• Partial Difference Sets
• On a Problem of D. R. Hughes
• SOME REMARKS ON VARIETIES OF GROUPS
• ON THE ASSOCIATED LIE RING OF A FREE 2-GENERATOR GROUP OF PRIME EXPONENT AND THE HUGHES CONJECTURE FOR 2-GENERATOR $ p$-GROUPS
• ON A CONNECTION BETWEEN HUGHES' CONJECTURE AND RELATIONS IN FINITE GROUPS OF PRIME EXPONENT
• The Hughes Problem and others
• On the H p -Problem for Finite p-Groups
• Solution of the Hughes Problem for Finite p-Groups of Class 2p - 2

This page was built for publication: On counterexamples to the Hughes conjecture.