Sylow-metacyclic groups andQ-admissibility
- Cite this article as:
- Chillag, D. & Sonn, J. Israel J. Math. (1981) 40: 307. doi:10.1007/BF02761371
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A finite groupG isQ-admissible if there exists a division algebra finite dimensional and central overQ which is a crossed product forG. AQ-admissible group is necessarily Sylow-metacyclic (all its Sylow subgroups are metacyclic). By means of an investigation into the structure of Sylow-metacyclic groups, the inverse problem (is every Sylow-metacyclic groupQ-admissible?) is essentially reduced to groups of order 2a 3b and to a list of known “almost simple” groups.