@article{oai:muroran-it.repo.nii.ac.jp:00009970,
 author = {TAKEGAHARA,  Yugen and 竹ケ原, 裕元},
 issue = {5},
 journal = {Communications in Algebra},
 month = {Feb},
 note = {application/pdf, Let $A$ be a finite group, and let $p$ be a prime. Suppose that $p^s$ is the highest power of $p$ dividing $|A/A'|$, where $A'$ is the commutator subgroup of $A$, and that the type $\lambda=(\lambda_1, \lambda_2,...)$ with $\lambda_1\geq\lambda_2\geq ...$ of a Sylow $p$-subgroup of $A/A'$ satisfies either $\lambda_2\leq1$ or $\lambda_2=2$ and $\lambda_3=0$. Let $m_A(d)$ denote the number of subgroups of index $d$ in $A$. If $1\leqi\leq[(s+1)/2]$ and $q$ is a positive integer such that $gcd(p,q)=1$, then $m_A(qp^{i-1})-m_A(qp^i)$ is a multiple of $p^i$ and $m_A(qp^{[(s+1)/2]})-m_A(qp^{[(s+1)/2]+1})$ is a multiple of $p^{[s/2]}$.},
 pages = {1964--1972},
 title = {The number of subgroups of a finite group (II)},
 volume = {47},
 year = {2019},
 yomi = {タケガハラ, ユウゲン}
}