{"id":554,"date":"2021-09-15T10:51:13","date_gmt":"2021-09-15T08:51:13","guid":{"rendered":"http:\/\/www1.karlin.mff.cuni.cz\/~kala\/web\/?page_id=554"},"modified":"2021-12-20T10:59:38","modified_gmt":"2021-12-20T09:59:38","slug":"21grupy","status":"publish","type":"page","link":"https:\/\/www1.karlin.mff.cuni.cz\/~kala\/web\/teaching\/21grupy","title":{"rendered":"\u00davod do teorie grup 2021\/22"},"content":{"rendered":"\t\t
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NMAG337<\/a>
Zimn\u00ed semestr 2020\/21
P\u0159edn\u00e1\u0161ka: pond\u011bl\u00ed 10:40 (v K1)
Cvi\u010den\u00ed: pond\u011bl\u00ed 9:00 (se mnou v K2, s Martinem Ra\u0161kou v K4)<\/p>

Podm\u00ednkou z\u00edsk\u00e1n\u00ed z\u00e1po\u010dtu je \u00fasp\u011b\u0161n\u00e9 vy\u0159e\u0161en\u00ed t\u0159\u00ed sad dom\u00e1c\u00edch \u00fakol\u016f. Po dohod\u011b je mo\u017en\u00e9 i opravn\u00e9 z\u00edsk\u00e1n\u00ed z\u00e1po\u010dtu za vy\u0159e\u0161en\u00ed v\u011bt\u0161\u00edho mno\u017estv\u00ed \u00fakol\u016f po term\u00ednu.<\/div>
Zisk z\u00e1po\u010dtu nen\u00ed t\u0159eba pro kon\u00e1n\u00ed zkou\u0161ky.<\/div>
Zkou\u0161ka bude \u00fastn\u00ed s cca. 60 minutami na p\u0159\u00edpravu dvou ot\u00e1zek odpov\u00eddaj\u00edc\u00edm l\u00e1tce z p\u0159edn\u00e1\u0161ek a cvi\u010den\u00ed (teorie a z\u00e1kladn\u00ed p\u0159\u00edklady). Viz term\u00edny vypsan\u00e9 v SISu a informace v diskusi.<\/div>
Covid<\/h6>

Na p\u0159edn\u00e1\u0161k\u00e1ch i cvi\u010den\u00edch pros\u00edm v\u0161echny o d\u016fsledn\u00e9 dodr\u017eov\u00e1n\u00ed koronavirov\u00fdch opat\u0159en\u00ed<\/span> – viz tady<\/a> a detailn\u011bji zejm\u00e9na tady<\/a>.
Konkr\u00e9tn\u011b na cvi\u010den\u00edch budeme v\u0161ichni m\u00edt respir\u00e1tory (cvi\u010d\u00edc\u00ed bude obch\u00e1zet studenty, tak\u017ee rozestupy nebudou mo\u017en\u00e9). I na p\u0159edn\u00e1\u0161ce ve velk\u00e9 K1 podle aktualizovan\u00fdch pravidel mus\u00ed m\u00edt v\u0161ichni studenti respir\u00e1tor<\/span>.
P\u0159edem d\u011bkuju.<\/p>

Konzultace<\/h6>

Pokud m\u00e1te z\u00e1jem o konzultaci (nebo m\u00e1te jak\u00e9koli dotazy nebo p\u0159ipom\u00ednky), dejte mi v\u011bd\u011bt osobn\u011b nebo mailem.<\/p>

Diskuse<\/a><\/h6>

je tady<\/a><\/p>

Dom\u00e1c\u00ed \u00fakoly<\/h6>

Sada 3<\/a> (do 20. prosince 9:00)
Sada 2<\/a> (do 22. listopadu 9:00)
Sada 1<\/a> (do\u00a0\u00a0 1. listopadu 9:00)<\/p>

Zad\u00e1n\u00ed zve\u0159ejn\u00edme v\u017edy aspo\u0148 2 t\u00fddny p\u0159ed term\u00ednem odevzd\u00e1n\u00ed.
Na z\u00e1po\u010det bude pot\u0159eba 75 % maxim\u00e1ln\u00edho po\u010dtu bod\u016f, \u010dili 45 bod\u016f.<\/p>

P\u0159edn\u00e1\u0161ka<\/h6>

\u00a0 3.\u00a0 1. p\u0159edn\u00e1\u0161ka ani cvi\u010den\u00ed nebudou, p\u0159edterm\u00edn zkou\u0161ky. Podrobn\u011bj\u0161\u00ed info ke konci semestru je v diskusi.<\/em>
20. 12. gener\u00e1tory podgrup voln\u00e9 grupy. Z\u00e1pisky<\/a>, video 1<\/a>, video 2<\/a>, video 3<\/a>, video 4<\/a> (p\u0159\u00edstupov\u00e9 \u00fadaje jsem pos\u00edlal mailem, p\u0159\u00edpadn\u011b mi je\u0161t\u011b napi\u0161te)<\/em>.\u00a0
13. 12. dokon\u010den\u00ed kone\u010dn\u011b generovan\u00fdch abelovsk\u00fdch grup,\u00a05.<\/strong> voln\u00e9 grupy a prezentace
\u00a0 6. 12. kone\u010dn\u011b generovan\u00e9 abelovsk\u00e9 grupy (dokon\u010den\u00ed kone\u010dn\u00fdch abelovsk\u00fdch p-grup, voln\u00e9 abelovsk\u00e9 grupy)
29. 11. dokon\u010den\u00ed nilpotence, 4. <\/strong>kone\u010dn\u011b generovan\u00e9 abelovsk\u00e9 grupy (torzn\u00ed podgrupa)
22. 11. pozn\u00e1mky k \u0159e\u0161itelnosti, centr\u00e1ln\u00ed \u0159ady, nilpotentn\u00ed grupy
15. 11. grupy \u0159\u00e1d\u016f 8 a 12, 3. <\/strong>subnorm\u00e1ln\u00ed \u0159ady, kompozi\u010dn\u00ed \u0159ady, Zassenhaus, Jordan-H\u00f6lder, \u0159e\u0161iteln\u00e9 grupy. Z\u00e1pisky<\/a>, video 1<\/a>, video 2<\/a> (p\u0159\u00edstupov\u00e9 \u00fadaje jsem pos\u00edlal mailem, p\u0159\u00edpadn\u011b mi je\u0161t\u011b napi\u0161te)<\/em>.
\u00a0 8. 11. Sylowovy v\u011bty, grupy \u0159\u00e1du pq
\u00a0 1. 11. jednoduchost A_n (dokon\u010den\u00ed na cvi\u010den\u00ed), 2. <\/strong>t\u0159\u00eddov\u00e1 rovnice a jej\u00ed d\u016fsledky, p-grupy
<\/em>18. 10. grupy \u0159\u00e1du 2p, automorfismy S_n, jednoduchost A_n (za\u010d\u00e1tek)
11. 10. dokon\u010den\u00ed komut\u00e1toru, automorfismy, direktn\u00ed a semidirektn\u00ed sou\u010din
\u00a0 4. 10. 1. <\/strong>v\u011bty o izomorfismu, komut\u00e1tor<\/p>

Cvi\u010den\u00ed<\/h6>

20. 12., 3. 1. cvi\u010den\u00ed nebudou<\/em>
13. 12.<\/a>
\u00a0 6. 12.<\/a>
29. 11.<\/a>
22. 11.<\/a>
\u00a0 8. 11.<\/a>
\u00a0 1. 11.<\/a>
25. 10.b<\/a>
25. 10.a<\/a>
18. 10.<\/a>
11. 10.<\/a>
\u00a0 4. 10.<\/a><\/p>

Pr\u016fb\u011bh kurzu bude podobn\u00fd roku 2017\/18<\/a>, ale na za\u010d\u00e1tku pojedeme v\u00fdrazn\u011b rychleji (proto\u017ee jsme tyto v\u011bci u\u017e prob\u00edrali na Algeb\u0159e; ur\u010dit\u011b doporu\u010duji si p\u0159ed za\u010d\u00e1tkem semestru zopakovat kapitolu IV ze skript<\/a>).<\/p>

Literatura<\/h6>

Joseph Rotman, An introduction to the theory of groups<\/em>, Springer, 1994 (Fourth edition). [prim\u00e1rn\u00ed zdroj]<\/em>
Ale\u0161 Dr\u00e1pal, Teorie grup – z\u00e1kladn\u00ed aspekty<\/em>, Karolinum, 2000.
J. S. Milne, Group Theory<\/em>, https:\/\/www.jmilne.org\/math\/CourseNotes\/gt.html<\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t

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NMAG337Zimn\u00ed semestr 2020\/21P\u0159edn\u00e1\u0161ka: pond\u011bl\u00ed 10:40 (v K1)Cvi\u010den\u00ed: pond\u011bl\u00ed 9:00 (se mnou v K2, s Martinem Ra\u0161kou v K4) Podm\u00ednkou z\u00edsk\u00e1n\u00ed z\u00e1po\u010dtu je \u00fasp\u011b\u0161n\u00e9 vy\u0159e\u0161en\u00ed t\u0159\u00ed sad dom\u00e1c\u00edch \u00fakol\u016f. Po dohod\u011b je mo\u017en\u00e9 i opravn\u00e9 z\u00edsk\u00e1n\u00ed z\u00e1po\u010dtu za vy\u0159e\u0161en\u00ed v\u011bt\u0161\u00edho mno\u017estv\u00ed \u00fakol\u016f po term\u00ednu.Zisk z\u00e1po\u010dtu nen\u00ed t\u0159eba pro kon\u00e1n\u00ed zkou\u0161ky.Zkou\u0161ka bude \u00fastn\u00ed s cca. 60 minutami…<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":51,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_kad_post_transparent":"default","_kad_post_title":"normal","_kad_post_layout":"default","_kad_post_sidebar_id":"","_kad_post_content_style":"default","_kad_post_vertical_padding":"top","_kad_post_feature":"hide","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_kad_post_classname":"","footnotes":""},"class_list":["post-554","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www1.karlin.mff.cuni.cz\/~kala\/web\/wp-json\/wp\/v2\/pages\/554","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www1.karlin.mff.cuni.cz\/~kala\/web\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www1.karlin.mff.cuni.cz\/~kala\/web\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www1.karlin.mff.cuni.cz\/~kala\/web\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www1.karlin.mff.cuni.cz\/~kala\/web\/wp-json\/wp\/v2\/comments?post=554"}],"version-history":[{"count":0,"href":"https:\/\/www1.karlin.mff.cuni.cz\/~kala\/web\/wp-json\/wp\/v2\/pages\/554\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www1.karlin.mff.cuni.cz\/~kala\/web\/wp-json\/wp\/v2\/pages\/51"}],"wp:attachment":[{"href":"https:\/\/www1.karlin.mff.cuni.cz\/~kala\/web\/wp-json\/wp\/v2\/media?parent=554"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}