Finite 2-Groups Whose Number of Subgroups of Each Order are at Most $2^4$

Abstract

Assume G is a group of order $2^n, n\ge 5$. Let $s_k(G)$ denote the number of subgroups of order $2^k$ of G. We classify finite 2-groups G with $s_k(G)\le 2^4,$ where $1\le k\le n$.

Keywords

Minimal nonabelian p-groups / Subgroup’s enumeration / Central extension

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Funding

NSFC(11471198)