The finite groups of cube-free order☆
The finite groups of cube-free order☆
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DOI：
10.1016/j.jalgebra.2011.02.040
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发表时间：
2011-05
影响因子：
0.9
通讯作者：
S. Qiao;Caiheng Li
中科院分区：
文献类型：
--
作者：
S. Qiao;Caiheng Li
A classical result of Hölder [4] tells us that a finite group of square-free order is exactly a group which has the form Zl: Zm, a semidirect product of a cyclic group Zl by a cyclic group Zm. In particular, a group of square-free order is meta-cyclic. A group is said to be of cube-free order if its order is not divisible by the cube of any prime. In 2005, H. Dietrich and B. Eick [2] investigated the class of groups of cube-free order, and among others, they presented an effective algorithm to classify the groups of cube-free order. For example, this algorithm has been used to determine the cube-free groups of order at most 10000. Also [2] shows that an unsolvable group G of cube-free order has the form G= PSL (2, p)× L with L being of odd order. The objective of this paper is to give a description for the class of groups of cube-free order, especially for solvable groups, which in some sense complements the work of [2]. The description is
