A remark on a Theorem of J. G. Thompson

Huppert, Bertram. "A remark on a Theorem of J. G. Thompson." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 9.3 (1998): 145-148. <http://eudml.org/doc/252350>.

@article{Huppert1998,
abstract = {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 \( p \).},
author = {Huppert, Bertram},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Lenght of conjugacy classes; p-lenght; finite groups; -solvable groups; -lengths; transitive permutation groups},
language = {eng},
month = {9},
number = {3},
pages = {145-148},
publisher = {Accademia Nazionale dei Lincei},
title = {A remark on a Theorem of J. G. Thompson},
url = {http://eudml.org/doc/252350},
volume = {9},
year = {1998},
}

TY - JOUR
AU - Huppert, Bertram
TI - A remark on a Theorem of J. G. Thompson
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1998/9//
PB - Accademia Nazionale dei Lincei
VL - 9
IS - 3
SP - 145
EP - 148
AB - 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 \( p \).
LA - eng
KW - Lenght of conjugacy classes; p-lenght; finite groups; -solvable groups; -lengths; transitive permutation groups
UR - http://eudml.org/doc/252350
ER -