A 2-block Splitting in Alternating Groups
نویسندگان
چکیده
In 1956, Brauer showed that there is a partitioning of the pregular conjugacy classes of a group according to the p-blocks of its irreducible characters with close connections to the block theoretical invariants. In a previous paper, the first explicit block splitting of regular classes for a family of groups was given for the 2-regular classes of the symmetric groups. Based on this work, here the corresponding splitting problem is investigated for the 2-regular classes of the alternating groups. As an application, an easy combinatorial formula for the elementary divisors of the Cartan matrix of the alternating groups at p = 2 is deduced.
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تاریخ انتشار 2009