# \(\mathbb{Z}_2\)

Last updated 2015-09-13 17:13:01 SGT»cyclic group of order two«

prove the following are true:

as a group it must be closed

per binary operations

one could, on this group, impose

extra structure (of a ring)

(but then its only ideal is itself)

(trivial) proper normal subgroup:

identity (that is, [\{\mathbb{I}\}])

one more subgroup, also normal:

the group itself (but also trivial)

this group has just two characters,

only one of which is faithful

all groups are associative;

this one much more so than others

finite, rational, nilpotent,

strongly ambivalent, simple —

symmetric?