Login to the T-machines using "putty" or "telnet t", at least one of which is installed on the computers in the office tower. From home you can download putty.exe, and then connect via "ssh" to "t.ms.uky.edu".
Now when you get to a prompt like "(~)t25% ", just type "gap" and hit return. You should see something like the log below, where blue is the human and green is the computer.
More information on GAP is available in its online reference manual or in the much shorter and easier to read learning material section. You can also download GAP for use on your own computer. Inside GAP, if you already know the name of the command you want information on, then ?commandname should give some help. Try ?Filtered for instance. If you do not know the name, but can make a guess as to part of the name, try ??part. For instance, try ??derived and ??commutator. Help search is case insensitive, but most of GAP is case sensitive.
(~)t25% gap GAP4, Version: 4.4.10 of 02-Oct-2007, i686-pc-linux-gnu-gcc Components: small 2.1, small2 2.0, small3 2.0, small4 1.0, small5 1.0, small6 1.0, small7 1.0, small8 1.0, small9 1.0, small10 0.2, id2 3.0, id3 2.1, id4 1.0, id5 1.0, id6 1.0, id9 1.0, id10 0.1, trans 1.0, prim 2.1 loaded. Packages: AClib 1.1, Polycyclic 2.2, Alnuth 2.2.5, nq 2.2, GAPDoc 1.1, CrystCat 1.1.2, Cryst 4.1.5, AutPGrp 1.2, CRISP 1.3.1, CTblLib 1.1.3, TomLib 1.1.2, FactInt 1.5.2, FGA 1.1.0.1, IRREDSOL 1.1.2, LAGUNA 3.4, Sophus 1.23, Polenta 1.2.7, ResClasses 2.5.3, AtlasRep 1.3.1, Browse 1.1, IO 2.3, cohomolo 1.4, EDIM 1.2.3, FORMAT 1.1, GRAPE 4.3, GrpConst 2.0, GUAVA 3.1, SONATA 2.3, kbmag 1.4, QuaGroup 1.3 loaded. gap> 1+1; 2 gap> (1,2,3)^2; (1,3,2) gap> 2^(1,2,3); 3 gap> (1,2)*(2,3); (1,3,2) gap> myd8 := Group( (1,2,3,4), (2,4) ); Group([ (1,2,3,4), (2,4) ]) gap> Order( myd8 ); 8 gap> IsAbelian( myd8 ); false gap> IsSolvable( myd8 ); true gap> IsNilpotent( myd8 ); true gap> Elements( myd8 ); [ (), (2,4), (1,2)(3,4), (1,2,3,4), (1,3), (1,3)(2,4), (1,4,3,2), (1,4)(2,3) ] gap> sym4 := SymmetricGroup( 4 ); Sym( [ 1 .. 4 ] ) gap> IsSubgroup( sym4, myd8 ); true gap> IsSubgroup( myd8, sym4 ); false gap> IsNormal( sym4, myd8 ); false gap> IsSubnormal( sym4, myd8 ); false gap> (1,2,3) in myd8; false gap> DerivedSubgroup( myd8 ) = Center( myd8 ); true gap> p := SylowSubgroup( sym4, 2 ); Group([ (1,2), (3,4), (1,3)(2,4) ]) gap> StructureDescription(p); "D8" gap> Order( p ); 8 gap> Elements( p ); [ (), (3,4), (1,2), (1,2)(3,4), (1,3)(2,4), (1,3,2,4), (1,4,2,3), (1,4)(2,3) ] gap> p = myd8; false gap> IsomorphismGroups( p, myd8 ); [ (1,2), (3,4), (1,3)(2,4) ] -> [ (2,4), (1,3), (1,2)(3,4) ] gap> IsomorphismGroups( sym4, myd8 ); fail gap> mylist := [1,2,3]; [ 1, 2, 3 ] gap> 1 in mylist; true gap> 4 in mylist; false gap> x -> x^2; function( x ) ... end gap> List( mylist, x -> x^2 ); [ 1, 4, 9 ] gap> List( myd8, x -> x^2 ); [ (), (), (), (1,3)(2,4), (), (), (1,3)(2,4), () ] gap> AsSet( List( myd8, x -> x^2 ) ); [ (), (1,3)(2,4) ] gap> Center( myd8 ); Group([ (1,3)(2,4) ]) gap> Elements( Center( myd8 ) ); [ (), (1,3)(2,4) ] gap> squares := AsSet( List( myd8, x -> x^2 ) ); [ (), (1,3)(2,4) ] gap> Reversed( squares ); [ (1,3)(2,4), () ] gap> squares = Center( myd8 ); true gap> Reversed( squares ) = Center( myd8 ); false gap> Filtered( myd8, x -> 4 = Order(x) ); [ (1,2,3,4), (1,4,3,2) ] gap> Filtered( sym4, x -> 4 = Order(x) ); [ (1,3,4,2), (1,4,2,3), (1,2,4,3), (1,4,3,2), (1,2,3,4), (1,3,2,4) ] gap> UpperCentralSeries( myd8 ); [ Group([ (1,3)(2,4), (2,4), (1,2,3,4) ]), Group([ (1,3)(2,4) ]), Group(()) ] gap> DerivedSeries( myd8 ); [ Group([ (1,2,3,4), (2,4) ]), Group([ (1,3)(2,4) ]), Group(()) ] gap> LowerCentralSeries( myd8 ); [ Group([ (1,2,3,4), (2,4) ]), Group([ (1,3)(2,4) ]), Group(()) ] gap> LowerCentralSeries( sym4 ); [ Sym( [ 1 .. 4 ] ), Group([ (1,3,2), (1,4,3) ]) ] gap> StructureDescription( sym4 ); "S4" gap> List( LowerCentralSeries( sym4 ), x -> StructureDescription( x ) ); [ "S4", "A4" ] gap> List( DerivedSeries( sym4 ), x -> StructureDescription( x ) ); [ "S4", "A4", "C2 x C2", "1" ] gap> List( ChiefSeries( sym4 ), x -> StructureDescription( x ) ); [ "S4", "A4", "C2 x C2", "1" ] gap> quit;