2017/06/29 by Benjamin Sambale, Sambale, Benjamin
Chemistry · Computer Science · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory #Representation Theory (math.RT) #Synthesis and Reactivity of Heterocycles
paper · pdf · doi:10.48550/arxiv.1706.09572
openalex publication_date 2017/06/29 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
Answering a question of P 'alfy and Pyber, we first prove the following\nextension of the k(GV)-Problem: Let G be a finite group and A\≤ Aut(G) such\nthat (|G|,|A|)=1. Then the number of conjugacy classes of the semidirect\nproduct GA is at most |G|. As a consequence we verify Brauer's k(B)-Conjecture\nfor pi-blocks of pi-separable groups which was proposed by Y. Liu. We also\ndiscuss equality in Brauer's Conjecture. On the other hand, we construct a\ncounterexample to a version of Olsson's Conjecture for pi-blocks which was also\nintroduced by Liu.\n