论文标题
具有环状或阿贝尔亚组的CLT组
CLT-groups with cyclic or abelian subgroups
论文作者
论文摘要
如果有限组包含对应于组的每个除数的子组，则称为CLT组。据说如果它包含与该组的每个适当分裂相对应的循环（Abelian）亚组，则是环状（Abelian）CLT组。如果该命令的每一组都是循环（Abelian）CLT组，则自然数字被认为是CCLT（ACLT）数字。在这项工作中，我们对所有CCLT和ACLT数字进行了分类，并研究了环状（Abelian）CLT组的各种特性。我们还表明，CCLT和ACLT组的类别包含在可超过的组类别中。此外，我们介绍了非循环有限组集的函数CCLT基准，并研究了该函数的属性。
A finite group is called a CLT-group if it contains a subgroup corresponding to every divisor of the order of the group. It is said to be a Cyclic (Abelian) CLT group if it contains a cyclic (abelian) subgroup corresponding to every proper divisor of the order of the group. A natural number is said to be a CCLT (ACLT) number if every group of that order is a cyclic (abelian) CLT group. In this work, we classify all CCLT and ACLT numbers and study various properties of Cyclic (Abelian) CLT groups. We also show that the classes of CCLT and ACLT groups are contained in the class of supersolvable groups. Moreover, we introduce the function CCLT-degree on the set of non-cyclic finite groups and study the properties of this function.
