منابع مشابه
Multiplicative Dedekind η-function and representations of finite groups
In this article we study the problem of finding such finite groups that the modular forms associated with all elements of these groups by means of a certain faithful representation belong to a special class of modular forms (so-called multiplicative η−products). This problem is open. We find metacyclic groups with such property and describe the Sylow p-subgroups, p 6= 2, for such groups. We als...
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In this paper we partially answer two open questions concerning clean rings. First, we demonstrate that if a quasi-continuous module is strongly clean then it is Dedekind-finite. Second, we prove a partial converse. We also prove that all clean decompositions on submodules of continuous modules extend to the entire module.
متن کاملA dedekind finite borel set
In this paper we prove three theorems about the theory of Borel sets in models of ZF without any form of the axiom of choice. We prove that if B ⊆ 2 is a Gδσ-set then either B is countable or B contains a perfect subset. Second, we prove that if 2 is the countable union of countable sets, then there exists an Fσδ set C ⊆ 2 such that C is uncountable but contains no perfect subset. Finally, we c...
متن کاملCharacterization of finite $p$-groups by the order of their Schur multipliers ($t(G)=7$)
Let $G$ be a finite $p$-group of order $p^n$ and $|{mathcal M}(G)|=p^{frac{1}{2}n(n-1)-t(G)}$, where ${mathcal M}(G)$ is the Schur multiplier of $G$ and $t(G)$ is a nonnegative integer. The classification of such groups $G$ is already known for $t(G)leq 6$. This paper extends the classification to $t(G)=7$.
متن کاملTABLE OF MARKS OF FINITE GROUPS
Let G be a finite group and C(G) be the family of representative conjugacy classes of subgroups of G. The matrix whose H;K-entry is the number of fixed points of the set G=K under the action of H is called the table of marks of G where H;K run through all elements in C(G). In this paper, we compute the table of marks and the markaracter table of groups of order pqr where p, q, r are prime numbers.
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1966
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s002776300001182x