\( \newcommand{\Implies}{\Rightarrow} \newcommand{\Iff}{\Leftrightarrow} \renewcommand{\emptyset}{\varnothing} \newcommand{\powersetsym}{\mathcal{P}} \newcommand{\fto}{\rightarrow} \newcommand{\mto}{\mapsto} \newcommand{\Cx}{\mathbb{C}} \newcommand{\R}{\mathbb{R}} \newcommand{\N}{\mathbb{N}} \newcommand{\Ns}{\mathbb{N}^*} \newcommand{\Z}{\mathbb{Z}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\K}{\mathbb{K}} \newcommand{\vv}[1]{\boldsymbol{#1}} \newcommand{\Abs}[1]{\left\lvert#1\right\rvert} \newcommand{\norm}[1]{ \left\|#1\right\| } \newcommand{\pnorm}[1]{\left\|#1\right\|_p} \newcommand{\supnorm}[1]{\left\|#1\right\|_\infty} \newcommand{\innerprod}[1]{\left\langle #1\right\rangle} \newcommand{\Ceil}[1]{\left\lceil #1\right\rceil} \newcommand{\Floor}[1]{\left\lfloor #1\right\rfloor} \newcommand{\Conj}[1]{\overline{#1}} \newcommand{\arccot}{\mathop{\text{arc\,cot}}\nolimits} \newcommand{\arcsec}{\mathop{\text{arc\,sec}}\nolimits} \newcommand{\arccsc}{\mathop{\text{arc\,csc}}\nolimits} \renewcommand{\arg}{\mathop{\text{arg}}\nolimits} \newcommand{\mcd}[1]{\mathop{\text{mcd}}\left(#1\right)} \newcommand{\mcm}[1]{\mathop{\text{mcm}}\left(#1\right)} \renewcommand{\ker}{\mathop{\text{ker}}\nolimits} \newcommand{\grad}{\mathop{\text{grad}}\nolimits} \newcommand{\dom}{\mathop{\text{dom}}\nolimits} \newcommand{\rng}{\mathop{\text{ran}}\nolimits} \newcommand{\diam}{\mathop{\text{diam}}\nolimits} \newcommand{\Obj}{\mathop{\text{obj}}\nolimits} \newcommand{\Hom}{\mathop{\text{hom}}\nolimits} \newcommand{\End}{\mathop{\text{end}}\nolimits} \newcommand{\Aut}[1]{\mathop{\mathrm{aut}}\nolimits(#1)} \newcommand{\Inn}[1]{\mathop{\mathrm{int}}\nolimits(#1)} \newcommand{\Deg}{\mathop{\mathrm{grad}}\nolimits} \newcommand{\Img}{\mathop{\text{im}}\nolimits} \newcommand{\Id}{\mathop{\mathrm{id}}\nolimits} \newcommand{\sgn}{\mathop{\mathrm{sgn}}\nolimits} \renewcommand{\Re}{\mathop{\mathrm{Re}}\nolimits} \renewcommand{\Im}{\mathop{\mathrm{Im}}\nolimits} \newcommand{\Char}{\mathop{\mathrm{car}}\nolimits} \renewcommand{\mod}[1]{\mathop{(\mathop{\text{mód}}\nolimits #1)}} \newcommand{\res}{\mathop{\text{mód}}} \newcommand{\categof}[1]{\mathsf{#1}} \newcommand{\CC}{\categof{C}} \newcommand{\CONJ}{\categof{Conj}} \newcommand{\SET}{\categof{Set}} \newcommand{\GRP}{\categof{Grp}} \newcommand{\AGRP}{\categof{Ab}} \newcommand{\morph}[1]{\mathrel{\mathop{\longrightarrow}\limits^{#1}}} \newcommand{\subgr}{\leq} \newcommand{\nsubgr}{\mathrel{\unlhd}} \newcommand{\iso}{\cong} \newcommand{\genby}[1]{\left\langle #1\right\rangle} \newcommand{\symgr}[1][n]{S_{#1}} \newcommand{\GenOf}[1]{\mathop{\text{gen}}\left(#1\right)} \newcommand{\normalizer}[2][G]{{\mathbf N}_{#1}(#2)} \newcommand{\centralizer}[2][G]{{\mathbf C}_{#1}(#2)} \newcommand{\orbit}[2][G]{\mathcal{O}_{#1}(#2)} \newcommand{\stab}[2][G]{#1(#2)} \newcommand{\GL}[2][n]{\mathrm{GL}(#1,#2)} \newcommand{\SL}[2][n]{\mathrm{SL}(#1,#2)} \newcommand{\Ort}[2][n]{\mathrm{O}(#1,#2)} \newcommand{\SO}[2][n]{\mathrm{SO}(#1,#2)} \newcommand{\KleinV}{\mathbf{V}}\)

Álgebra abstracta

Rubén Maguregui

Índice general
1 Números enteros
1.1 Divisibilidad
1.2 La identidad de Bézout
1.3 Números primos
1.4 Congruencias
2 Grupos
2.1 Operaciones binarias; semigrupos y monoides
2.2 Grupos
2.3 Permutaciones
2.4 Subgrupos
2.5 Homomorfismos
2.6 Grupos cíclicos
2.7 Clases laterales; el teorema de Lagrange
Bibliografía
Índice alfabético