The Schur Multipliers of the Mathieu Groups
نویسندگان
چکیده
منابع مشابه
THE STRUCTURE OF FINITE ABELIAN p-GROUPS BY THE ORDER OF THEIR SCHUR MULTIPLIERS
A well-known result of Green [4] shows for any finite p-group G of order p^n, there is an integer t(G) , say corank(G), such that |M(G)|=p^(1/2n(n-1)-t(G)) . Classifying all finite p-groups in terms of their corank, is still an open problem. In this paper we classify all finite abelian p-groups by their coranks.
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 کاملSchur Multipliers of n-engel Groups
We find a bound for the exponent of the Schur multiplier of a finite p-group in terms of the exponent and Engel length of the given group. It is also proved that if G is a 3-Engel group of finite exponent, then the exponent of H2(G) divides exp G. When G is a 4-Engel group of exponent e, the exponent of H2(G) divides 10e.
متن کاملSchur Multipliers of the Known Finite Simple Groups
In this note, we announce some results about the Schur multipliers of the known finite simple groups. Proofs will appear elsewhere. We shall conclude with a summary of current knowledge on the subject. Basic properties of multipliers and covering groups of finite groups are discussed in [6]. Notation for groups of Lie type is standard [3], [8]. G' denotes the commutator subgroup of the group G,...
متن کاملOn Schur Multipliers of Pairs and Triples of Groups with Topological Approach
In this paper, using a relation between Schur multipliers of pairs and triples of groups, the fundamental group and homology groups of a homotopy pushout of Eilenberg-MacLane spaces, we present among other things some behaviors of Schur multipliers of pairs and triples with respect to free, amalgamated free, and direct products and also direct limits of groups with topological approach.
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 1966
ISSN: 0027-7630,2152-6842
DOI: 10.1017/s0027763000026519