scholarly journals STRONGLY INVARIANT SUBGROUPS

2014 ◽  
Vol 57 (2) ◽  
pp. 431-443 ◽  
Author(s):  
GRIGORE CĂLUGĂREANU
Keyword(s):  
Abelian Groups ◽  
Fully Invariant Subgroups ◽  
Special Case

AbstractAs a special case of fully invariant subgroups, strongly invariant subgroups are introduced and studied for Abelian groups.

scholarly journals On fully invariant subgroups of primary abelian groups.

1976 ◽  
Vol 22 (3) ◽  
pp. 281-284 ◽  
Author(s):  
Ronald C. Linton
Keyword(s):  
Abelian Groups ◽  
Fully Invariant Subgroups

Solution of a Problem of L. Fuchs Concerning Finite Intersections of Pure Subgroups

1986 ◽  
Vol 38 (2) ◽  
pp. 304-327 ◽  
Author(s):  
R. Göbel ◽  
R. Vergohsen
Keyword(s):  
Finite Number ◽  
Abelian Groups ◽  
Natural Numbers ◽  
P 75 ◽  
Image Position ◽  
Special Case

L. Fuchs states in his book “Infinite Abelian Groups” [6, Vol. I, p. 134] the followingProblem 13. Find conditions on a subgroup of A to be the intersection of a finite number of pure (p-pure) subgroups of A.The answer to this problem will be given as a special case of our theorem below. In order to find a better setting of this problem recall that a subgroup S ⊆ E is p-pure if pnE ∩ S = pnS for all natural numbers. Then S is pure in E if S is p-pure for all primes p. This generalizes to pσ-isotype, a definition due to L. J. Kulikov, cf. [6, Vol. II, p. 75] and [11, pp. 61, 62]. If α is an ordinal, then S is pσ-isotype if

The Homological Functors of Some Abelian Groups of Prime Power Order

2014 ◽  
Vol 71 (5) ◽  
Author(s):  
Rosita Zainal ◽  
Nor Muhainiah Mohd Ali ◽  
Nor Haniza Sarmin ◽  
Samad Rashid
Keyword(s):  
Tensor Product ◽  
Prime Power ◽  
Homotopy Theory ◽  
Abelian Groups ◽  
Prime Power Order ◽  
Schur Multiplier ◽  
Integer Coefficients ◽  
Nonabelian Tensor ◽  
Tensor Square ◽  
Special Case

The homological functors of a group were first introduced in homotopy theory. Some of the homological functors including the nonabelian tensor square and the Schur multiplier of abelian groups of prime power order are determined in this paper. The nonabelian tensor square of a group G introduced by Brown and Loday in 1987 is a special case of the nonabelian tensor product. Meanwhile, the Schur multiplier of G is the second cohomology with integer coefficients is named after Issai Schur. The aims of this paper are to determine the nonabelian tensor square and the Schur multiplier of abelian groups of order p5, where p is an odd prime

scholarly journals On Automorphisms of Direct Products of Cayley Graphs on Abelian Groups

10.37236/9940 ◽  
2021 ◽  
Vol 28 (3) ◽  
Author(s):  
Dave Witte Morris
Keyword(s):  
Direct Product ◽  
Abelian Groups ◽  
Cayley Graphs ◽  
Direct Products ◽  
Special Case

Let $X$ and $Y$ be connected Cayley graphs on abelian groups, such that no two distinct vertices of $X$ have exactly the same neighbours, and the same is true about $Y$. We show that if the number of vertices of $X$ is relatively prime to the number of vertices of $Y$, then the direct product $X \times Y$ has only the obvious automorphisms (namely, the ones that come from automorphisms of its factors $X$ and $Y$). This was not previously known even in the special case where $Y = K_2$ has only two vertices. The proof of this special case is short and elementary. The general case follows from the special case by standard arguments.

On the Isomorphism of Integral Group Rings. II

1969 ◽  
Vol 21 ◽  
pp. 1182-1188 ◽  
Author(s):  
Sudarshan K. Sehgal
Keyword(s):  
Normal Subgroup ◽  
Abelian Groups ◽  
Group Rings ◽  
Integral Group ◽  
Integral Group Rings ◽  
Normal Abelian Subgroup ◽  
Ordered Groups ◽  
Free Abelian Groups ◽  
Special Case ◽  
Torsion Free

Let Z(G) denote the integral group ring of a group G. Let be the class of groups G with the property that for any isomorphism θ: Z(G) → Z(H), we have θ(g) = ±h, h ∈ H, for all g ∈ G. We study this class in § 2 and establish that it contains classes of torsion-free abelian groups, torsion abelian groups, and ordered groups.In § 4, we prove the following result.THEOREM. Let G be a group which contains a normal abelian subgroup A such that. Suppose that θ: Z(G) → Z(H) is an isomorphism such that θ(Δ(G, A)) = Δ(H, B) for a suitable normal subgroup B of H. Then G ≃ H. (Here Δ(G, A) is the kernel of the natural map Z(G) → Z(G/A).)Jackson (3) and Whitcomb (6) proved the special case of this theorem when G is supposed to be finite metabelian. The lemmas needed are given in §3.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

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