论文标题
用少量子组分类组
Classifying groups with a small number of subgroups
论文作者
论文摘要
我们提供了组$ g $的子组数量的下限，这是出现在$ | g | $的主要分解中的素数和指数的函数。使用这些边界，我们将所有亚伯利亚组分类为22个或更少的亚组，以及所有具有19个或更少亚组的非阿布尔组。这使我们可以扩展由Slattery在\ cite {slattery}中引入的整数a274847 \ cite {oeis}。
We provide lower bounds on the number of subgroups of a group $G$ as a function of the primes and exponents appearing in the prime factorization of $|G|$. Using these bounds, we classify all abelian groups with 22 or fewer subgroups, and all non-abelian groups with 19 or fewer subgroups. This allows us to extend the integer sequence A274847 \cite{OEIS} introduced by Slattery in \cite{Slattery}.
