Normal Abelian subgroups and Euler characteristic
نویسندگان
چکیده
منابع مشابه
Characteristic Subgroups of Finite Abelian Groups
We consider the question: When do two finite abelian groups have isomorphic lattices of characteristic subgroups? An explicit description of the characteristic subgroups of such groups enables us to give a complete answer to this question in the case where at least one of the groups has odd order. An “exceptional” isomorphism, which occurs between the lattice of characteristic subgroups of Zp ×...
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In this paper we prove that a finite group $G$ having at most three conjugacy classes of non-normal non-abelian proper subgroups is always solvable except for $Gcong{rm{A_5}}$, which extends Theorem 3.3 in [Some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable, Acta Math. Sinica (English Series) 27 (2011) 891--896.]. Moreover, we s...
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Fully invariant subgroups of an Abelian p-group have been the object of a good deal of study, while characteristic subgroups have received somewhat less attention. Recently the socles of fully invariant subgroups have been studied and this led to the notion of a socle-regular group. The present work replaces the fully invariant subgroups with characteristic ones and leads in a natural way to th...
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Suppose G is an arbitrary additively written primary abelian group with a fixed large subgroup L. It is shown that G is (a) summable; (b) σ -summable; (c) a Σ-group; (d) pω+1-projective only when so is L. These claims extend results of such a kind obtained by Benabdallah, Eisenstadt, Irwin and Poluianov, Acta Math. Acad. Sci. Hungaricae (1970) and Khan, Proc. Indian Acad. Sci. Sect. A (1978).
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 1989
ISSN: 0022-4049
DOI: 10.1016/0022-4049(89)90084-4