$
\let\vuoto\varnothing
\let\setminus\smallsetminus
\let\iso\simeq
\let\n\triangleleft
\let\implica\Rightarrow
\let\Implica\Longrightarrow
\let\shiff\Leftrightarrow
\let\immersione\hookrightarrow
\let\epi\twoheadrightarrow
\let\mono\rightarrowtail
\let\ot\otimes
\newcommand\set[1]{\{#1\}}
\newcommand\P{{\mathscr P}}
\newcommand\U{{\mathscr U}}
\newcommand\I{{\mathcal I}}
\newcommand\F{{\mathcal F}}
% \newcommand\Pf{{\P_{\mbox{\small\textbf {fin}}}}}
\newcommand\Pf{{\P_{\text{fin}}}}
\newcommand\N{\mathbb N}
\newcommand\Z{\mathbb Z}
\newcommand\Q{\mathbb Q}
\newcommand\R{\mathbb R}
\newcommand\C{\mathbb C}
\newcommand\S{\mathbb S}
\newcommand\Pr{\mathbb P}
\newcommand\ds{\mathbin{\scriptstyle\triangle}}
\newcommand\xor{\mathbin{\mathsf{XOR}}}
\newcommand\nor{\mathbin{\mathsf{NOR}}}
\newcommand\nand{\mathbin{\mathsf{NAND}}}
\newcommand\gen[1]{\langle#1\rangle}
\DeclareMathOperator{\id}{id}
\DeclareMathOperator{\im}{im}
\DeclareMathOperator{\rest}{rest}
\DeclareMathOperator{\Sym}{Sym}
\DeclareMathOperator{\Div}{Div}
\DeclareMathOperator{\Corr}{Corr}
\DeclareMathOperator{\Rel}{Rel}
\DeclareMathOperator{\Map}{Map}
\DeclareMathOperator{\Eq}{Eq}
\DeclareMathOperator{\Part}{Part}
\DeclareMathOperator{\partz}{Partz}
\DeclareMathOperator{\OS}{OS}
\DeclareMathOperator{\OL}{OL}
\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\jac}{Jac}
\DeclareMathOperator{\nrad}{NilRad}
\DeclareMathOperator{\ann}{Ann}
\DeclareMathOperator{\ass}{Ass}
\DeclareMathOperator{\Min}{Min}
\DeclareMathOperator{\minor}{Minor}
\DeclareMathOperator{\maggior}{Maggior}
\DeclareMathOperator{\var}{Var}
\DeclareMathOperator{\spec}{Spec}
\DeclareMathOperator{\car}{char}
\DeclareMathOperator{\cd}{cd}
\newcommand\Mod{{\mathcal{Mod}}}
% \DeclareRobustCommand {\modbin}{\mathbin{\textrm {mod}}}
\newcommand\modbin {\mathbin{\textrm {mod}}}
\newcommand\antivec[2] {#1^{\raise #2pt\hbox{$\!\!\scriptstyle\leftarrow\!\!$}}}
\newcommand\antivecf{\antivec f3}
\newcommand\antivecv{v^{\raise 1.2pt\hbox{$\!\!\!\scriptstyle\leftarrow\!\!$}}}
\newcommand\antivecg{g^{\raise 2pt\hbox{$\!\!\!\scriptstyle\leftarrow\!\!$}}}
\newcommand\vecvuoto {\vec{\phantom{p}}}
\newcommand\antivecvuoto{\,\antivec {{}}{2}}
% \newcommand\antivecvuoto{{}^{\raise 2pt\hbox{$\scriptstyle\leftarrow\!\!$}}}
\newcommand\maxid{\mathbin{{\n}{\cdot}}}
\let\sseq\subseteq
$
Abstract
The object of this work is to find classes of groups which possess only countably many maximal subgroups. Modules with countably many maximal submodules and
group rings having countably many maximal right ideals are also investigated. Examples of soluble groups with uncountably many maximal subgroups are described.
Dismiss