My OperaProgress Saturday
Saturday, December 17, 2005 10:48:09 PM
Worked on the character table of C3 x S3. Did not complete it due to time constraints but I felt much more comfortable working on character tables than a while back. I should, must, want to complete a few tables real soon.
A start, at last...! Sym^2 V = The subspace of V (x) V fixed under s. I found a definition. Pfff. What is s? Will see later. I really thought I would never understand that stuff. I blame it under 'poorly documented' stuff.
Associative Algebras . Learned about a new algebraic structure today. Not really new because I have worked a lot with instances of this structure like the n x n matrices and the quaternions.
*** ALERT! *** Today I stumbled over the following group while I was doing some simple calculations:
gap> StructureDescription(AllGroups(32)[8]);
"C2 . ((C4 x C2) : C2) = (C2 x C2) . (C4 x C2)"
I knew of the Group Direct Product and Semi-direct Product, how I can use them in GAP, and how I can construct them manually. It is however the first time that I see a group description in this sort of format. I checked the GAP Reference and found that it had to with 'splitting extensions'. To make a long story short: I found ( a lot of ?? ) uncovered ground in Group Theory. I didn't expect such a surprise with a group of only order 32. To Do? Group Extension , Wreath Product , Hall Subgroup , , Nilpotent Group , Frattini Subgroup , Fitting Subgroup to start with. I have to plan this stuff.
A start, at last...! Sym^2 V = The subspace of V (x) V fixed under s. I found a definition. Pfff. What is s? Will see later. I really thought I would never understand that stuff. I blame it under 'poorly documented' stuff.
Associative Algebras . Learned about a new algebraic structure today. Not really new because I have worked a lot with instances of this structure like the n x n matrices and the quaternions.
*** ALERT! *** Today I stumbled over the following group while I was doing some simple calculations:
gap> StructureDescription(AllGroups(32)[8]);
"C2 . ((C4 x C2) : C2) = (C2 x C2) . (C4 x C2)"
I knew of the Group Direct Product and Semi-direct Product, how I can use them in GAP, and how I can construct them manually. It is however the first time that I see a group description in this sort of format. I checked the GAP Reference and found that it had to with 'splitting extensions'. To make a long story short: I found ( a lot of ?? ) uncovered ground in Group Theory. I didn't expect such a surprise with a group of only order 32. To Do? Group Extension , Wreath Product , Hall Subgroup , , Nilpotent Group , Frattini Subgroup , Fitting Subgroup to start with. I have to plan this stuff.
