It is proved that if the degree of any non-linear irreducible character of a finite group G is a product of powers of two given distinct prime integers p and q, then G has an abelian Hall {p, q} subgroup H and an Abel...It is proved that if the degree of any non-linear irreducible character of a finite group G is a product of powers of two given distinct prime integers p and q, then G has an abelian Hall {p, q} subgroup H and an Abelian normal {p, q} complement A, and the centralizer in A of the Sylow p-subgroup of G is equal to the centralizer in A of the Sylow q-subgroup of G.展开更多
All groups considered in this note are finite. Let π be a set of some primes and π′ the complementary set of primes, π(G) denotes the set of primes dividing the order |G| of a group G.
文摘It is proved that if the degree of any non-linear irreducible character of a finite group G is a product of powers of two given distinct prime integers p and q, then G has an abelian Hall {p, q} subgroup H and an Abelian normal {p, q} complement A, and the centralizer in A of the Sylow p-subgroup of G is equal to the centralizer in A of the Sylow q-subgroup of G.
基金Project supported by the Natural Science Fund of Shanxi Province
文摘All groups considered in this note are finite. Let π be a set of some primes and π′ the complementary set of primes, π(G) denotes the set of primes dividing the order |G| of a group G.
