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A remark on a Theorem of J. G. Thompson

Bertram Huppert (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

An important theorem by J. G. Thompson says that a finite group G is p -nilpotent if the prime p divides all degrees (larger than 1) of irreducible characters of G . Unlike many other cases, this theorem does not allow a similar statement for conjugacy classes. For we construct solvable groups of arbitrary p -lenght, in which the lenght of any conjugacy class of non central elements is divisible by p .

Algorithms for permutability in finite groups

Adolfo Ballester-Bolinches, Enric Cosme-Llópez, Ramón Esteban-Romero (2013)

Open Mathematics

In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.

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