Assertion: group | /r/HasProperty | isomorphic
Facets:
value: to the simple group
type: OTHER
value: to z/6z = {0,1,2,3,4,5}
type: OTHER
value: with the operation of addition
type: OTHER
value: to z/nz
type: LOCATION
value: with corresponding to k.
type: OTHER
value: to the integers
type: OTHER
Source sentences:
text: By the fundamental theorem of finite abelian groups, the group ( Z / n Z ) × {\displaystyle (\mathbb {Z} /n\mathbb {Z} )^{\times }} is isomorphic to a direct product of cyclic groups of prime power orders.
text: Two groups G and H are called isomorphic if there exist group homomorphisms a:
text: This group is isomorphic to the integers.
text: Such a group is also isomorphic to Z/nZ, the group of integers modulo n with the addition operation, which is the standard cyclic group in additive notation.
text: These groups are also isomorphic to Z/6Z = {0,1,2,3,4,5} with the operation of addition modulo 6, with zk and gk corresponding to k.
text: If p is a prime number, then any group with p elements is isomorphic to the simple group Z/pZ.