Research Information System
ARCHIV DER MATHEMATIK, vol.113, no.6, pp.561-563, 2019 (SCI-Expanded)
Let H be a subgroup of a finite group G, and suppose that H contains a Sylow p-subgroup P of G. Write N=NG(H)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N = \mathbf{N}_{G}(H)$$\end{document}, and assume that the Sylow p-subgroups of H boolean AND Hg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H \cap H<^>g$$\end{document} are cyclic for all elements g is an element of G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g \in G$$\end{document} not lying in N. We show that in this situation, N controls G-fusion in P.