The Orbit Graph of Finite p-Groups and Groups of Order pq
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.
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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 $t(G)=7$.
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For two distinct primes p, q, we describe those clones on a set of size pq that contain a given group operation and all constants operations. We show that each such clone is determined by congruences and commutator relations. Thus we obtain that there is only a finite number of such clones on a fixed set.
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ژورنال
عنوان ژورنال: Indian Journal of Science and Technology
سال: 2014
ISSN: 0974-6846,0974-5645
DOI: 10.17485/ijst/2014/v7i12.12