0000000000205365

AUTHOR

J. Miquel Martínez

showing 2 related works from this author

An infinite family of counterexamples to a conjecture on positivity

2021

Recently, G. Mason has produced a counterexample of order 128 to a conjecture in conformal field theory and tensor category theory in [Ma]. Here we easily produce an infinite family of counterexamples, the smallest of which has order 72.

Frobenius–Schur indicatorPure mathematicsAlgebra and Number TheoryConjectureConformal field theoryTensor (intrinsic definition)Order (group theory)Geometry and TopologyCategory theoryMathematical PhysicsAnalysisMathematicsCounterexampleRendiconti del Seminario Matematico della Università di Padova
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Degrees of characters in the principal block

2021

Abstract Let G be a finite group. We prove that if the set of degrees of characters in the principal p-block of G has size at most 2 then G is p-solvable, and G / O p ′ ( G ) has a metabelian normal Sylow p-subgroup. The general question of proving that if an arbitrary p-block has two degrees then their defect groups are metabelian remains open.

Set (abstract data type)CombinatoricsFinite groupAlgebra and Number Theory010102 general mathematics0103 physical sciencesSylow theoremsPrincipal (computer security)Block (permutation group theory)010307 mathematical physics0101 mathematics01 natural sciencesMathematicsJournal of Algebra
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