Sentences with AUTOMORPHISM
Check out our example sentences below to help you understand the context.Sentences
1
"The automorphism group of a graph"
1
"An automorphism of a group G is an isomorphism from G to itself."
2
"The group of all automorphisms of G, denoted by Aut(G), forms a group under composition of functions."
3
"The automorphism group of a graph is the group of all automorphisms of the graph."
4
"In linear algebra, the automorphism group of a vector space is the group of all bijective linear transformations from the space to itself."
5
"The automorphism group of a field is the group of all automorphisms from the field to itself."
6
"In group theory, an automorphism can preserve the order of elements in a group."
7
"An inner automorphism is an automorphism of the form g(x) = gxg⁻¹ for some fixed element g."
8
"An automorphism can map an element to its inverse."
9
"An automorphism can fix certain elements while permuting others."
10
"Certain groups have non-trivial automorphisms."
11
"The automorphism group of a cyclic group is isomorphic to the multiplicative group of integers modulo n, where n is the order of the group."
12
"The automorphism group of a complete graph is the symmetric group on its vertices."
13
"An automorphism of a lattice can preserve the meet and join operations."
14
"The automorphism group of a tree is always a solvable group."
15
"The automorphism group of a planar graph can be non-trivial."
1
"The automorphism of a graph is a symmetry-preserving bijection of its vertices onto themselves."
2
"In abstract algebra, an automorphism is an isomorphism from a mathematical object to itself."
3
"An automorphism of a set is a permutation of the elements that preserves the set's structure."
4
"The automorphism group of a regular polyhedron consists of symmetries that preserve its shape."
5
"An automorphism of a field is a bijective homomorphism from the field to itself."
6
"The automorphisms of a group form a mathematical structure called an automorphism group."
7
"An automorphism of a directed graph is a bijection that preserves the direction of edges."
8
"The set of automorphisms of a regular polygon can be seen as rotations and reflections."
9
"In graph theory, automorphisms are used to analyze the structural properties of graphs."
