منابع مشابه
Basic Subgroups in Commutative Modular Group Rings
Let S(RG) be a normed Sylow p-subgroup in a group ring RG of an abelian group G with p-component Gp and a p-basic subgroup B over a commutative unitary ring R with prime characteristic p. The first central result is that 1 + I(RG;Bp) + I(R(p)G;G) is basic in S(RG) and B[1 + I(RG;Bp) + I(R(p )G;G)] is p-basic in V (RG), and [1 + I(RG;Bp) + I(R(p )G;G)]Gp/Gp is basic in S(RG)/Gp and [1 + I(RG;Bp)...
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In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the s...
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We establish a correspondence between abelian regular subgroup of the affine group, and commutative, associative algebra structures on the underlying vector space that are (Jacobson) radical rings. As an application, we show that if the underlying field has positive characteristic, then an abelian regular subgroup has finite exponent if the vector space is finite-dimensional, while it can be to...
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It is shown that in the units of augmentation one of an integral group ring ZG of a finite group G, a noncyclic subgroup of order p, for some odd prime p, exists only if such a subgroup exists in G. The corresponding statement for p = 2 holds by the Brauer–Suzuki theorem, as recently observed by W. Kimmerle.
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We establish a link between abelian regular subgroup of the affine group, and commutative, associative algebra structures on the underlying vector space that are (Jacobson) radical rings. As an application, we show that if the underlying field has positive characteristic , then an abelian regular subgroup has finite exponent if the vector space is finite-dimensional, while it can be torsion fre...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 2002
ISSN: 0011-4642,1572-9141
DOI: 10.1023/a:1021779506416