Skip to main content
Contents
Embed
Dark Mode Prev Up Next
\(\require{mathtools}\require{color} \setcounter{MaxMatrixCols}{15}
\newcommand{\mbu}[1]{\mathbf{\mathrm{#1}}}
\newcommand{\N}{\mathbb N}
\newcommand{\Z}{\mathbb Z}
\newcommand{\Q}{\mathbb Q}
\newcommand{\R}{\mathbb R}
\newcommand{\cC}{\mathcal{C}}
\newcommand{\F}{\mathbb{F}}
\newcommand{\GF}{\mathrm{GF}}
\DeclareMathOperator{\Span}{Span}
\DeclareMathOperator{\rank}{rank}
\DeclareMathOperator{\lcm}{lcm}
\DeclareMathOperator{\rk}{rk}
\DeclareMathOperator{\wt}{wt}
\DeclareMathOperator{\im}{im}
\makeatletter
\@ifundefined{char}{
\DeclareMathOperator{\char}{char}
}{}
\makeatother
\DeclareMathOperator{\GRS}{GRS}
\DeclareMathOperator{\RS}{RS}
\DeclareMathOperator{\BCH}{BCH}
\newcommand{\transpose}[1]{#1^{\top}}
\newcommand{\by}{\mathbf{y}}
\newcommand{\bc}{\mathbf{c}}
\newcommand{\bx}{\mathbf{x}}
\newcommand{\bm}{\mathbf{m}}
\newcommand{\bs}{\mathbf{s}}
\newcommand{\be}{\mathbf{e}}
\newcommand{\bu}{\mathbf{u}}
\newcommand{\bv}{\mathbf{v}}
\newcommand{\bh}{\mathbf{h}}
\newcommand{\br}{\mathbf{r}}
\newcommand{\bzero}{\mathbf{0}}
\newcommand{\balpha}{\boldsymbol{\alpha}}
\newcommand{\subgroup}[1]{\langle{#1}\rangle}
\newcommand{\isom}{\cong}
\DeclareMathOperator\Aut{Aut}
\DeclareMathOperator\Char{char}
\DeclareMathOperator\cl{cl}
\DeclareMathOperator\Conj{Conj}
\DeclareMathOperator\Inn{Inn}
\DeclareMathOperator\Gal{Gal}
\DeclareMathOperator\Out{Out}
\DeclareMathOperator\orb{orb}
\DeclareMathOperator\Orb{Orb}
\DeclareMathOperator\Perm{Perm}
\DeclareMathOperator\stab{stab}
\DeclareMathOperator\Stab{Stab}
\DeclareMathOperator\fix{fix}
\DeclareMathOperator\Fix{Fix}
\DeclareMathOperator\Syl{Syl}
\DeclareMathOperator\Sym{Sym}
\DeclareMathOperator\soc{soc}
\DeclareMathOperator{\nil}{nil}
\DeclareMathOperator{\Nil}{Nil}
\DeclareMathOperator\jac{jac}
\DeclareMathOperator\Jac{Jac}
\DeclareMathOperator\Eq{Eq}
\DeclareMathOperator\Hol{Hol}
\DeclareMathOperator\Frac{Frac}
\DeclareMathOperator\GL{GL}
\DeclareMathOperator\SL{SL}
\DeclareMathOperator\So{SO}
\DeclareMathOperator\SU{SU}
\DeclareMathOperator\PGL{PGL}
\DeclareMathOperator\PSL{PSL}
\DeclareMathOperator\PSU{PSU}
\DeclareMathOperator\PSP{PsP}
\DeclareMathOperator\AGL{AGL}
\DeclareMathOperator\Heis{Heis}
\DeclareMathOperator\Dic{Dic}
\DeclareMathOperator\SA{SA}
\DeclareMathOperator\SD{SD}
\DeclareMathOperator\Fr{Fr}
\DeclareMathOperator\Mod{Mod}
\DeclareMathOperator\DQ{DQ}
\DeclareMathOperator\QD{QD}
\DeclareMathOperator\OD{OD}
\DeclareMathOperator\Cl{Cl}
\DeclareMathOperator\BinTet{2T}
\DeclareMathOperator\BinOct{2O}
\DeclareMathOperator\BinIcos{2I}
\DeclareMathOperator\Aff{Aff}
\DeclareMathOperator\BS{BS}
\newcommand{\normal}{\lhd}
\newcommand{\normaleq}{\unlhd}
\newcommand{\nnormal}{\ntriangleleft}
\newcommand{\nnormaleq}{\ntrianglelefteq}
\def\longto{\longrightarrow}
\def\into{\hookrightarrow}
\def\longinto{\longhookrightarrow}
\def\onto{\twoheadrightarrow}
\DeclareRobustCommand\longonto{\relbar\joinrel\twoheadrightarrow}
\DeclareMathOperator{\Image}{Im}
\DeclareMathOperator\Ker{Ker}
\DeclareMathOperator{\Id}{Id}
\newcommand{\ceil}[1] {\left\lceil #1 \right\rceil}
\newcommand{\floor}[1] {\left\lfloor #1 \right\rfloor}
\definecolor{xRed}{RGB}{229, 31, 58}
\definecolor{xBlue}{RGB}{68, 119, 170}
\definecolor{xGreen}{RGB}{33, 135, 51}
\definecolor{xPurple}{RGB}{170, 51, 119}
\definecolor{xOrange}{RGB}{ 197, 83, 17}
\newcommand{\lt}{<}
\newcommand{\gt}{>}
\newcommand{\amp}{&}
\newcommand{\fillinmath}[1]{\mathchoice{\underline{\displaystyle \phantom{\ \,#1\ \,}}}{\underline{\textstyle \phantom{\ \,#1\ \,}}}{\underline{\scriptstyle \phantom{\ \,#1\ \,}}}{\underline{\scriptscriptstyle\phantom{\ \,#1\ \,}}}}
\)
Chapter Module 2: Cosets, Maps, and Quotients
In this module, we’ll learn about the cosets of a subgroup, maps between groups, and the connections between these objects and quotient groups. From this page you can navigate to the daily prep assignments, notes, and activities. The notes here are not a substitute for attending class or reading the textbook. To access printable versions of the activities with space to work, use the print icon in the top right of each activity page.