- DF Section 2.4 #9 #17 (Zorn’s lemma appears in Appendix 1), #18
- DF Section 3.1 #1, #12.
- Let F be any field. Show that there is a 1-1 homormophism from to $GL(n,F)$ given by the action of on the indices i in the standard basis . Combine this with Cayley’s theorem (page 120) to show that for every finite group G, there exists n, such that G is isomorphic to a subgroup of .
- Show algebraically that every isometry T of is a glide reflection provided it has the form $\latex T=T_\lambda A$, where $A\in O(2,R)$, $A\not\in SO(2,R)$, $\latex \lambda\ne 0$.
- Solve the following problems without submitting a solution
- DF Section 2.4 #15, #19

Advertisements
(function(){var c=function(){var a=document.getElementById("crt-702373414");window.Criteo?(a.parentNode.style.setProperty("display","inline-block","important"),a.style.setProperty("display","block","important"),window.Criteo.DisplayAcceptableAdIfAdblocked({zoneid:388248,containerid:"crt-702373414",collapseContainerIfNotAdblocked:!0,callifnotadblocked:function(){a.style.setProperty("display","none","important");a.style.setProperty("visbility","hidden","important")}})):(a.style.setProperty("display","none","important"),a.style.setProperty("visibility","hidden","important"))};if(window.Criteo)c();else{if(!__ATA.criteo.script){var b=document.createElement("script");b.src="//static.criteo.net/js/ld/publishertag.js";b.onload=function(){for(var a=0;a<__ATA.criteo.cmd.length;a++){var b=__ATA.criteo.cmd[a];"function"===typeof b&&b()}};(document.head||document.getElementsByTagName("head")[0]).appendChild(b);__ATA.criteo.script=b}__ATA.criteo.cmd.push(c)}})();
(function(){var c=function(){var a=document.getElementById("crt-1150489753");window.Criteo?(a.parentNode.style.setProperty("display","inline-block","important"),a.style.setProperty("display","block","important"),window.Criteo.DisplayAcceptableAdIfAdblocked({zoneid:837497,containerid:"crt-1150489753",collapseContainerIfNotAdblocked:!0,callifnotadblocked:function(){a.style.setProperty("display","none","important");a.style.setProperty("visbility","hidden","important")}})):(a.style.setProperty("display","none","important"),a.style.setProperty("visibility","hidden","important"))};if(window.Criteo)c();else{if(!__ATA.criteo.script){var b=document.createElement("script");b.src="//static.criteo.net/js/ld/publishertag.js";b.onload=function(){for(var a=0;a<__ATA.criteo.cmd.length;a++){var b=__ATA.criteo.cmd[a];"function"===typeof b&&b()}};(document.head||document.getElementsByTagName("head")[0]).appendChild(b);__ATA.criteo.script=b}__ATA.criteo.cmd.push(c)}})();