TY - JOUR
AU1 - Lu, Jiakuan
AU2 - Wang, Yu
AU3 - Zhang, Boru
AU4 - Meng, Wei
AB - For a finite group G, let s(G) denote the number of subgroups of G and d(G) denote the number of divisors of |G|. In this paper, we prove that there does not exist a finite group G such that d(G)<s(G)<d(G)+p1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$d(G)<s(G)<d(G)+p_1$$\end{document}, where p1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$p_1$$\end{document} is the smallest prime divisor of |G|, and determine the structure of finite groups G such that s(G)=d(G)+p1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$s(G) = d(G) + p_1$$\end{document}.
TI - On the number of subgroups of a finite group
JF - Ricerche di Matematica
DO - 10.1007/s11587-022-00738-w
DA - 2024-09-01
UR - https://www.deepdyve.com/lp/springer-journals/on-the-number-of-subgroups-of-a-finite-group-rB7OF0em0T
SP - 1867
EP - 1872
VL - 73
IS - 4
DP - DeepDyve
ER -