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ON THE CHARACTERISTIC DEGREE OF FINITE GROUPS
In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...
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The least cardinal λ such that some (equivalently: every) compact group with weight α admits a dense, pseudocompact subgroup of cardinality λ is denoted by m(α). Clearly, m(α) ≤ 2. We show: Theorem 3.3. Among groups of cardinality γ, the group ⊕γQ serves as a “test space” for the availability of a pseudocompact group topology in this sense: If m(α) ≤ γ ≤ 2 then ⊕γQ admits a (necessarily connect...
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Let C be a class of topological abelian groups and SPC denote the full subcategory of subobjects of products of objects of C. We say that SPC has Mackey coreflections if there is a functor that assigns to each object A of SPC an object τA that has the same group of characters as A and is the finest topology with that property. We show that the existence of Mackey coreflections in SPC is equival...
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1969
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700042180