# group axiom in a sentence

1) Thus a

**group**homomorphism respects all the structure of "G" provided by the

**group**

**axioms**.

2) With the proper generalization of the

**group**

**axioms**this gives rise to an "n"-ary group.

axiom collocations

3) The following properties of integer addition serve as a model for the abstract

**group**

**axioms**given in the definition below.

4) The only

**group**

**axiom**that requires some effort to verify is that each element of "G" is invertible.

## group axiom example sentences

5) Two important consequences of the**group**

**axioms**are the uniqueness of the identity element and the uniqueness of inverse elements.

6) The study of

**group**homomorphisms then provides a tool for studying general properties of

**groups**and consequences of the

**group**

**axioms**.

7) This means that we have a smooth multiplication μ : G × G → G, an inversion ν : G → G and a unit element e ∈ G such that the usual

**group**

**axioms**are satisfied.

8) It can be shown that all other relations among the braids __FORMULA__ and __FORMULA__ already follow from these relations and the

**group**

**axioms**.

9) In the case above, the inverse of 4 is 4, and the inverse of 3 is 2, as . Hence all

**group**

**axioms**are fulfilled.

10) Basic facts about all

**groups**that can be obtained directly from the

**group**

**axioms**are commonly subsumed under "elementary

**group**theory".

11) Indeed the four

**group**

**axioms**are satisfied:

12) and thus the transformation matrix, consistent with the

**group**

**axioms**, is given by

13) Given this set of symmetries and the described operation, the

**group**

**axioms**can be understood as follows:

14) To qualify as a group, the set and operation,, must satisfy four requirements known as the "

**group**

**axioms**":

### example sentences with axiom

15) To qualify as an abelian group, the set and operation,, must satisfy five requirements known as the "abelian**group**

**axioms**":

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