“…(2) G possesses an H-injector and any two H-injectors are conjugate in G; All unexplained notion and terminology are standard. The reader is referred to [3,8,2].…”
Section: Theorem 15 Let H Be a Hartley Set Of A Group G Defined By Amentioning
Let G be a group and H be a Hartley set of G. In this paper, we prove the existence and conjugacy of H-injectors of G and describe the structure of the injectors. As application, some known results are directly followed.
“…(2) G possesses an H-injector and any two H-injectors are conjugate in G; All unexplained notion and terminology are standard. The reader is referred to [3,8,2].…”
Section: Theorem 15 Let H Be a Hartley Set Of A Group G Defined By Amentioning
Let G be a group and H be a Hartley set of G. In this paper, we prove the existence and conjugacy of H-injectors of G and describe the structure of the injectors. As application, some known results are directly followed.
Let σ = {σ i |i ∈ I} be some partition of the set of all primes P, G a finite group and σ(G) = {σ i |σ i ∩ π(G) = ∅}. A set H of subgroups of G is said to be a complete Hall σ-set of G if every member = 1 of H is a Hall σ i -subgroup of G for some σ i ∈ σ and H contains exact one Hall σ i -subgroup of G for every σ i ∈ σ(G).
In this paper, we prove the existence and conjugacy of injectors of a generalized π-soluble groups for the Hartley class defined by a invariable Hartley function, and give a description of the structure of the injectors.
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