Automorphism in a sentence
Synonym: transformation.
Meaning: A transformation of a mathematical structure that preserves its form.
(1) Bilection is used to define automorphism.
(2) The automorphism group of a cube has 48 elements.
(3) The automorphism group of a finite field is cyclic.
(4) The automorphism of a graph preserves its structure.
(5) An automorphism is a self-mapping of a mathematical object.
(6) The automorphism of a tree is a permutation of its vertices.
(7) An automorphism of a poset is a bijective order-preserving map.
(8) The automorphism group of a connected graph is always non-trivial.
(9) The automorphism group of a complete graph is its symmetric group.
(10) An automorphism can be represented by a permutation in combinatorics.
Automorphism sentence
(11) An automorphism of a group is an isomorphism from the group to itself.
(12) The automorphisms of a graph can be used to find its automorphism set.
(13) An automorphism of a vector space is a bijective linear transformation.
(14) The automorphisms of a graph can be used to find its automorphism size.
(15) The automorphisms of a graph can be used to find its automorphism group.
(16) The automorphisms of a graph can be used to find its automorphism orbit.
(17) The automorphisms of a graph can be used to find its automorphism class.
(18) The automorphisms of a graph can be used to find its automorphism cycle.
(19) The automorphisms of a graph can be used to find its automorphism order.
(20) The automorphisms of a graph can be used to find its automorphism number.
Automorphism make sentence
(21) The automorphisms of a graph can be used to find its automorphism degree.
(22) An automorphism can be represented by a permutation group in group theory.
(23) An automorphism of a metric space is an isometry from the space to itself.
(24) The automorphisms of a graph can be used to find its automorphism subgroup.
(25) The automorphisms of a graph can be used to find its automorphism property.
(26) An automorphism of a category is an isomorphism from the category to itself.
(27) An automorphism can be represented by a permutation matrix in linear algebra.
(28) The automorphisms of a graph can be used to find its automorphism polynomial.
(29) The concept of endomorphism is closely related to the concept of automorphism.
(30) The automorphism of a graph can be used to study its symmetries and properties.
Sentence of automorphism
(31) The automorphism group of a regular polygon is isomorphic to the dihedral group.
(32) The automorphism group of a directed graph is a subgroup of its symmetric group.
(33) The automorphisms of a graph can be used to find its automorphism transformation.
(34) The automorphism of a monoid can be used to study its endomorphisms and submonoids.
(35) An automorphism of a topological space is a homeomorphism from the space to itself.
(36) An automorphism can be thought of as a symmetry of an object that leaves it unchanged.
(37) The automorphism of a tree can be used to study its branching patterns and connectivity.
(38) The automorphism of a lattice can be used to study its order-preserving transformations.
(39) The automorphism of a manifold can be used to study its diffeomorphisms and smooth maps.
(40) The automorphism of a hypergraph can be used to study its edge-preserving transformations.
Automorphism meaningful sentence
(41) The automorphisms of a group form a mathematical structure known as an automorphism group.
(42) The concept of automorphism is widely used in algebraic structures such as rings and fields.
(43) The automorphism of a group can be used to study its conjugacy classes and normal subgroups.
(44) The automorphism group of a finite group is isomorphic to a subgroup of its symmetric group.
(45) The automorphism of a directed graph can be used to study its arc-preserving transformations.
(46) An automorphism can be thought of as a self-mapping that preserves the structure of an object.
(47) The automorphism of a semigroup can be used to study its idempotent-preserving transformations.
(48) An automorphism of a hypergraph is a permutation of its vertices that preserves the hyperedges.
(49) An automorphism of a matroid is a permutation of its elements that preserves the rank function.
(50) The automorphism group of a connected graph is isomorphic to a subgroup of its symmetric group.
Automorphism sentence examples
(51) The automorphism of a permutation group can be used to analyze its cycle structure and symmetry.
(52) The automorphism group of a regular polytope is isomorphic to a subgroup of the symmetric group.
(53) The automorphism group of a regular polyhedron is isomorphic to a subgroup of the symmetric group.
(54) The automorphism of a topological space can be used to study its homeomorphisms and continuous maps.
(55) The automorphism group of a finite abelian group is isomorphic to a direct product of cyclic groups.
(56) The automorphism of a vector space can be used to study its linear transformations and basis changes.
(57) The automorphism group of a connected planar graph is isomorphic to a subgroup of its symmetric group.
(58) The automorphism group of a regular tiling of the plane is isomorphic to a subgroup of the Euclidean group.
(59) The automorphism group of a mathematical object consists of all the automorphisms that can be applied to it.
(60) The automorphism of a poset can be used to study its order-preserving transformations and lattice properties.
(61) An automorphism can be thought of as a self-homeomorphism that preserves the topological properties of an object.
(62) The automorphism group of a regular tessellation of the plane is isomorphic to a subgroup of the Euclidean group.
(63) An automorphism is a mathematical concept used to describe a transformation that preserves the structure of an object.
Automorphism meaning
Automorphism is a term that is commonly used in mathematics and computer science. It refers to a type of function that maps a mathematical object onto itself, while preserving its structure. In other words, an automorphism is a transformation that leaves the object unchanged in terms of its properties and characteristics. If you are looking to use the word "automorphism" in a sentence, there are a few tips that can help you to do so effectively. Here are some suggestions:
1. Understand the meaning of the word: Before you attempt to use the word "automorphism" in a sentence, it is important to have a clear understanding of what it means. This will help you to use it correctly and in the appropriate context. As mentioned earlier, an automorphism is a function that preserves the structure of a mathematical object. This could be a group, a ring, a field, or any other type of mathematical structure.
2. Use it in a technical context: Since "automorphism" is a technical term, it is best used in a technical context.
For example, you might use it in a sentence that describes a mathematical proof or a computer algorithm. This will help to ensure that your use of the word is accurate and appropriate.
3. Provide context: When using the word "automorphism" in a sentence, it is important to provide context so that your reader understands what you are referring to.
For example, you might say "The automorphism group of a ring is the set of all automorphisms that preserve the ring's structure." This sentence provides context by explaining what the automorphism group is and what it does.
4. Use it sparingly: While "automorphism" is a useful term in mathematics and computer science, it is not a word that should be used excessively. If you use it too often, it can become repetitive and lose its impact. Instead, try to use it only when it is necessary to convey a specific meaning or concept.
5. Practice using it: Like any technical term, using "automorphism" in a sentence takes practice. Try writing sentences that use the word in different contexts, and ask a colleague or mentor to review them for accuracy and clarity. With practice, you will become more comfortable using the word and incorporating it into your technical writing.
In conclusion, "automorphism" is a technical term that is commonly used in mathematics and computer science. To use it effectively in a sentence, it is important to understand its meaning, use it in a technical context, provide context, use it sparingly, and practice using it. By following these tips, you can use "automorphism" with confidence and clarity in your technical writing.
The word usage examples above have been gathered from various sources to reflect current and historical usage of the word Automorphism. They do not represent the opinions of TranslateEN.com.