From add2e4969d20d292612e89e626d0f2ec95857340 Mon Sep 17 00:00:00 2001 From: Hearot Date: Mon, 23 Oct 2023 20:14:53 +0200 Subject: [PATCH] feat(algebra1): aggiunge la teoria sui gruppi liberi e sulle presentazioni --- .../main.pdf | Bin .../main.tex | 0 .../2. Il prodotto semidiretto/main.pdf | Bin .../2. Il prodotto semidiretto/main.tex | 0 .../3. Gruppi liberi e presentazioni/main.pdf | Bin 0 -> 175850 bytes .../3. Gruppi liberi e presentazioni/main.tex | 91 ++++++++++++++++++ .../1. Il gruppo degli automorfismi/main.pdf | Bin 243582 -> 245190 bytes .../1. Il gruppo degli automorfismi/main.tex | 5 +- 8 files changed, 95 insertions(+), 1 deletion(-) rename Secondo anno/Algebra 1/Teoria dei gruppi/{Costruzioni di gruppo (prodotti di sottogruppi e semidiretti) => Costruzioni di gruppo (prodotti di sottogruppi, semidiretti e presentazioni)}/1. Prodotto di sottogruppi e ordini di gruppi abeliani/main.pdf (100%) rename Secondo anno/Algebra 1/Teoria dei gruppi/{Costruzioni di gruppo (prodotti di sottogruppi e semidiretti) => Costruzioni di gruppo (prodotti di sottogruppi, semidiretti e presentazioni)}/1. Prodotto di sottogruppi e ordini di gruppi abeliani/main.tex (100%) rename Secondo anno/Algebra 1/Teoria dei gruppi/{Costruzioni di gruppo (prodotti di sottogruppi e semidiretti) => Costruzioni di gruppo (prodotti di sottogruppi, semidiretti e presentazioni)}/2. Il prodotto semidiretto/main.pdf (100%) rename Secondo anno/Algebra 1/Teoria dei gruppi/{Costruzioni di gruppo (prodotti di sottogruppi e semidiretti) => Costruzioni di gruppo (prodotti di sottogruppi, semidiretti e presentazioni)}/2. Il prodotto semidiretto/main.tex (100%) create mode 100644 Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi, semidiretti e presentazioni)/3. Gruppi liberi e presentazioni/main.pdf create mode 100644 Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi, semidiretti e presentazioni)/3. Gruppi liberi e presentazioni/main.tex diff --git a/Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi e semidiretti)/1. Prodotto di sottogruppi e ordini di gruppi abeliani/main.pdf b/Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi, semidiretti e presentazioni)/1. Prodotto di sottogruppi e ordini di gruppi abeliani/main.pdf similarity index 100% rename from Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi e semidiretti)/1. Prodotto di sottogruppi e ordini di gruppi abeliani/main.pdf rename to Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi, semidiretti e presentazioni)/1. Prodotto di sottogruppi e ordini di gruppi abeliani/main.pdf diff --git a/Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi e semidiretti)/1. Prodotto di sottogruppi e ordini di gruppi abeliani/main.tex b/Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi, semidiretti e presentazioni)/1. Prodotto di sottogruppi e ordini di gruppi abeliani/main.tex similarity index 100% rename from Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi e semidiretti)/1. Prodotto di sottogruppi e ordini di gruppi abeliani/main.tex rename to Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi, semidiretti e presentazioni)/1. Prodotto di sottogruppi e ordini di gruppi abeliani/main.tex diff --git a/Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi e semidiretti)/2. Il prodotto semidiretto/main.pdf b/Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi, semidiretti e presentazioni)/2. Il prodotto semidiretto/main.pdf similarity index 100% rename from Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi e semidiretti)/2. Il prodotto semidiretto/main.pdf rename to Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi, semidiretti e presentazioni)/2. Il prodotto semidiretto/main.pdf diff --git a/Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi e semidiretti)/2. Il prodotto semidiretto/main.tex b/Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi, semidiretti e presentazioni)/2. Il prodotto semidiretto/main.tex similarity index 100% rename from Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi e semidiretti)/2. Il prodotto semidiretto/main.tex rename to Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi, semidiretti e presentazioni)/2. Il prodotto semidiretto/main.tex diff --git a/Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi, semidiretti e presentazioni)/3. Gruppi liberi e presentazioni/main.pdf b/Secondo anno/Algebra 1/Teoria dei gruppi/Costruzioni di gruppo (prodotti di sottogruppi, semidiretti e presentazioni)/3. 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Il gruppo degli automorfismi/main.tex b/Secondo anno/Algebra 1/Teoria dei gruppi/Gruppi classici (Aut(G), Sn, Dn, G_ab, Q8)/1. Il gruppo degli automorfismi/main.tex index 945391e..4d827bf 100644 --- a/Secondo anno/Algebra 1/Teoria dei gruppi/Gruppi classici (Aut(G), Sn, Dn, G_ab, Q8)/1. Il gruppo degli automorfismi/main.tex +++ b/Secondo anno/Algebra 1/Teoria dei gruppi/Gruppi classici (Aut(G), Sn, Dn, G_ab, Q8)/1. Il gruppo degli automorfismi/main.tex @@ -149,7 +149,10 @@ \begin{example}[$\Aut(S_3) \cong S_3$] - Si osserva che $Z(S_3)$ deve essere obbligatoriamente + Si\footnote{ + Vale un fatto molto più generale: $\Aut(S_n) \cong S_n$ + per ogni $n \geq 3$ con $n \neq 6$. + } osserva che $Z(S_3)$ deve essere obbligatoriamente banale\footnote{ In generale $Z(S_n)$ è banale per $n \geq 3$. }. Infatti, se non lo fosse, $Z(S_3)$ potrebbe