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Sunday, October 23, 2005

Groups of order 18

There are 5 groups of order 18:

gap> grp(18);
Group 1 has structure: D18 and is Non-Abelian
Group 2 has structure: C18 and is Abelian
Group 3 has structure: C3 x S3 and is Non-Abelian
Group 4 has structure: (C3 x C3) : C2 and is Non-Abelian
Group 5 has structure: C6 x C3 and is Abelian

The workhorse here is the function ConstructAllGroups and is part of the GAP package GrpConst.

# Prints all groups of order n
# IN: Group
local listGroups;
while(i<(Length(listGroups)+1)) do
Print("Group ");
Print(" has structure: ");
Print(" and is ");
if (IsAbelian(listGroups[i])) then

Sunday, October 2, 2005


Whatever you have to do with a structure-endowed entity S try to determine its group of automorphisms . . . You can expect to gain a deep insight into the constitution of S in this way.
Herman Weyl, Symmetry ( Quote found in this PDF )

Is it possible to translate the above sentence to "Jip en Janneke"-language? Before anything else I should give it a try myself.

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(Raumpatrouille – Die phantastischen Abenteuer des Raumschiffes Orion, colloquially aka Raumpatrouille Orion was the first German science fiction television series. Its seven episodes were broadcast by ARD beginning September 17, 1966. The series has since acquired cult status in Germany. Broadcast six years before Star Trek first aired in West Germany (in 1972), it became a huge success.)