Loop of exponent two
This article defines a property that can be evaluated for a loop.
View other properties of loops
A nontrivial loop is termed a loop of exponent two if the square of every element in the loop is the identity element of the loop.
Whether we consider the trivial loop a loop of exponent two is a moot point.
An example that is non-abelian (and not a group) is the loop of order five and exponent two.
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|Power-associative loop||powers are well-defined, independent of parenthesization|||FULL LIST, MORE INFO|
|Left nuclear square loop||every square element is in the left nucleus|||FULL LIST, MORE INFO|
|Middle nuclear square loop||every square element is in the middle nucleus|||FULL LIST, MORE INFO|
|Right nuclear square loop||every square element is in the right nucleus|||FULL LIST, MORE INFO|