The isomorphic description of torsion units in commutative group rings over fields with positive characteristic.
Danchev, Peter (2004)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Danchev, Peter (2004)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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Derek J. S. Robinson (2006)
Rendiconti del Seminario Matematico della Università di Padova
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Danchev, P. (2003)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: Primary 20C07, 20K10, 20K20, 20K21; Secondary 16U60, 16S34. Let PG be the abelian modular group ring of the abelian group G over the abelian ring P with 1 and prime char P = p. In the present article,the p-primary components Up(PG) and S(PG) of the groups of units U(PG) and V(PG) are classified for some major classes of abelian groups. Suppose K is a first kind field with respect to p in char K ≠ p and A is an abelian p-group. In the...
Peter Vassilev Danchev (2003)
Commentationes Mathematicae Universitatis Carolinae
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A new class of abelian -groups with all high subgroups isomorphic is defined. Commutative modular and semisimple group algebras over such groups are examined. The results obtained continue our recent statements published in Comment. Math. Univ. Carolinae (2002).
B. Wehrfritz (2007)
Open Mathematics
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Let G be a hypercyclic group. The most substantial results of this paper are the following. a) If G/G′ is 2-divisible, then G is 2-divisible. b) If G/G′ is a 2′-group, then G is a 2′-group. c) If G/G′ is divisible by finite-of-odd-order, then G/V is divisible by finite-of-odd-order, where V is the intersection of the lower central series (continued transfinitely) of O 2′ (G).
K. Kaarli, L. Márki (2004)
Rendiconti del Seminario Matematico della Università di Padova
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R. S. Pierce, C. I. Vinsonhaler (1990)
Rendiconti del Seminario Matematico della Università di Padova
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B. Wehrfritz (2007)
Open Mathematics
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Let G be a hypercentral group. Our main result here is that if G/G’ is divisible by finite then G itself is divisible by finite. This extends a recent result of Heng, Duan and Chen [2], who prove in a slightly weaker form the special case where G is also a p-group. If G is torsion-free, then G is actually divisible.
A. M. Aghdam, A. Najafizadeh (2009)
Colloquium Mathematicae
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Let G be an abelian group and ◻ G its square subgroup as defined in the introduction. We show that the square subgroup of a non-homogeneous and indecomposable torsion-free group G of rank two is a pure subgroup of G and that G/◻ G is a nil group.