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* An (infix) binary operation +, called addition. * An (infix) binary operation *, called multiplication. ... ...

* The associativity of the binary operation * The existence of a neutral ... Power-associative binary operation A binary operation is said to be ... ...

Suppose (S,*) is a magma, i.e., S is a set and * is a binary operation ... A power-associative magma is a magma satisfying the following equivalent ... ...

* An (infix) binary operation +, called the addition * An (infix) binary operation *, called the multiplication ... ...

| Stronger than::Power-associative magma || powers are well-defined || || || power-associative magma|diassociative magma |- | Stronger than::Flexible ... ...

A hypergroup is a set G equipped with a binary operation *: G \times ... we note that * can be extended to an operation 2^G \times 2^G \to 2^G ... ...

# A group can be defined as a set with three operations: a binary ... # A group can also be defined as a set with an associative binary ... ...

An algebra loop L with binary operation * is said to be a left Bol ... | Stronger than::Power-associative loop || powers are well-defined ... ...

Let S be a set and * be a binary operation on S (viz, * is a map S ... Let S be a set and f: S \times S \to S be a binary operation. We say ... ...

A binary linear code is a vector subspace W of the power set of a finite set X. Here, the power set of a finite set is treated as a vector space ... ...

##* General definition of binary operation ##* Definition of commutative binary operation ##* Definition of associative ... ...

* Magma: Set with binary operation * Semigroup: Set with associative binary operation * Monoid: Set with ... ...

* Binary operation: Closure under the binary operation is already given to us. * Identity element e \in H: Since H is nonempty, there exists some ... ...

M: There's an operation called multiplication, where basically ... change? Like a group evolving through constant operation? ... ...

F(F(x,y),z) as formal power series || If F is the binary operation denoting multiplication, then F is associative. |- | 2 || Identity element ... ...

* Magma: A set with a binary operation. * Semigroup: A set with an associative binary operation. ... ...

monoid with inverses, set with associative binary operation having ... A group is a set G with a binary operation *: G \times G \to G (termed ... ...

the Lie brackets are replaced by an arbitrary binary operation and the coefficient for any product of n terms is 2^{n-1} times its coefficient in ... ...

| binary octahedral group || 48 || 1,2,8,24,48 || 1,2,6,24,48 || subgroup ... subgroups forms a lattice with the meet operation being intersection of subgroups ... ...

leq n^{n^2}, because this is simply the number of binary operations from a set to itself. A better bound that can be proven using elementary methods ... ...