منابع مشابه
on the representation theory of the alternating groups
we present the basic results on the representation theory of the alternating groups. our approach is based on clifford theory.
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In a recent paper Külshammer, Olsson, Robinson gave a danalogue for the Nakayama conjecture for symmetric groups where d ≥ 2 is an arbitrary integer. We prove that there is a natural d-analogue of the Nakayama conjecture for alternating groups whenever d is 2 or an arbitrary odd integer greater than 1. This generalizes an old result of Kerber.
متن کاملOn Alternating and Symmetric Groups as Galois Groups
Fix an integer n = 3. We show that the alternating group An appears as Galois group over any Hilbertian field of characteristic different from 2. In characteristic 2, we prove the same when n is odd. We show that any quadratic extension of Hilbertian fields of characteristic different from 2 can be embedded in an Sn–extension (i.e. a Galois extension with the symmetric group Sn as Galois group)...
متن کاملOn character tables related to the alternating groups
There is a simple formula for the absolute value of the determinant of the character table of the symmetric group Sn. It equals aP , the product of all parts of all partitions of n (see [4, Corollary 6.5]). In this paper we calculate the absolute values of the determinants of certain submatrices of the character table X of the alternating group An, including that of X itself (Section 2). We als...
متن کاملOn the validity of Thompson’s conjecture for alternating groups
Let G be a group. Let π(G) be the set of prime divisor of |G|. Let GK(G) denote the graph with vertex set π(G) such that two primes p and q in π(G) are joined by an edge if G has an element of order p · q. We use s(G) to denote the number of connected components of the prime graph GK(G). Let N(G) be the set of nonidentity orders of conjugacy classes of elements in G. Some authors have proved th...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1970
ISSN: 0021-8693
DOI: 10.1016/0021-8693(70)90132-8