what is the cayley table for the symmetries of an isosceles triangle?
2007-03-21 19:59:31 · 2 answers · asked by Marva S 1 in Science & Mathematics ➔ Mathematics
A Cayley table describes the structure of a group, say G = { g1, ..., gn} with operation *, by displaying a table in which the ith row and the jth column contains the product gi*gj. In essence, the Cayley table is the group-theoretic analogue of an addition or a multiplication table. Cayley tables are named after the mathematician Arthur Cayley.
Cayley originally set up his "squares" so that the identity element was first, giving rise to the first row and column acting as column headers. One can also depict Cayley tables with separate row and column indices.
For example, the Cayley table of the cyclic group of order 3 is as follows:
a b c
b c a
c a b
where a is the identity element, and c = b2.
The table tells us that cb = bc = a, for example.
2007-03-21 20:11:53 · answer #1 · answered by reden 2 · 0⤊ 0⤋
The only symmetry I see is one reflection, so it's just a cyclic group with two elements.
Doing the table for that is easy!
2007-03-22 03:35:09 · answer #2 · answered by Curt Monash 7 · 0⤊ 0⤋