Let be a finite group and denote the set of complex irreducible character degrees of . In this paper, we prove that if is a finite group and is an almost simple group whose socle is a Mathieu group such that , then there exists an abelian subgroup of such that is isomorphic to . In view of Huppert's conjecture (2000), we also provide some examples to show that is not necessarily a direct product of and , and hence we cannot extend this conjecture to almost simple groups.
Publié le :
DOI : 10.4171/RSMUP/138-6
DOI : 10.4171/RSMUP/138-6
Classification :
20
Mots-clés : Character degrees, almost simple groups, sporadic simple groups, Mathieu simple groups, Huppert’s conjecture
Mots-clés : Character degrees, almost simple groups, sporadic simple groups, Mathieu simple groups, Huppert’s conjecture
Affiliations des auteurs :
Alavi, Seyed Hassan 1 ;
Daneshkah, Ashraf 1 ;
Jafari, Ali 1
@article{RSMUP_2017__138__115_0, author = {Alavi, Seyed Hassan and Daneshkah, Ashraf and Jafari, Ali}, title = {On groups with the same character degrees as almost simple groups with socle {Mathieu} groups}, journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova}, pages = {115--127}, publisher = {European Mathematical Society Publishing House}, address = {Zuerich, Switzerland}, volume = {138}, year = {2017}, doi = {10.4171/RSMUP/138-6}, mrnumber = {3743248}, zbl = {1380.20007}, url = {http://www.numdam.org/articles/10.4171/RSMUP/138-6/} }
TY - JOUR AU - Alavi, Seyed Hassan AU - Daneshkah, Ashraf AU - Jafari, Ali TI - On groups with the same character degrees as almost simple groups with socle Mathieu groups JO - Rendiconti del Seminario Matematico della Università di Padova PY - 2017 SP - 115 EP - 127 VL - 138 PB - European Mathematical Society Publishing House PP - Zuerich, Switzerland UR - http://www.numdam.org/articles/10.4171/RSMUP/138-6/ DO - 10.4171/RSMUP/138-6 ID - RSMUP_2017__138__115_0 ER -
%0 Journal Article %A Alavi, Seyed Hassan %A Daneshkah, Ashraf %A Jafari, Ali %T On groups with the same character degrees as almost simple groups with socle Mathieu groups %J Rendiconti del Seminario Matematico della Università di Padova %D 2017 %P 115-127 %V 138 %I European Mathematical Society Publishing House %C Zuerich, Switzerland %U http://www.numdam.org/articles/10.4171/RSMUP/138-6/ %R 10.4171/RSMUP/138-6 %F RSMUP_2017__138__115_0
Alavi, Seyed Hassan; Daneshkah, Ashraf; Jafari, Ali. On groups with the same character degrees as almost simple groups with socle Mathieu groups. Rendiconti del Seminario Matematico della Università di Padova, Tome 138 (2017), pp. 115-127. doi : 10.4171/RSMUP/138-6. http://www.numdam.org/articles/10.4171/RSMUP/138-6/
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