Thread: Symmetry groups are indecomposible

Show that symmetry group of n letters is indecomposible where n>2.

The definition of decomposible is "If G is decomposible group, G can be written as internal direct product of two nontrivial subgroups of G".

thanks!!!

Originally Posted by chipai

Show that symmetry group of n letters is indecomposible where n>2.

The definition of decomposible is "If G is decomposible group, G can be written as internal direct product of two nontrivial subgroups of G".

thanks!!!

For n=3,4 show directly, and for n > 4 remember that S_n has ONLY one non-trivial normal sbgp., namely A_n...

Tonio