| 单词 |
automorphism |
| 释义 |
autoˈmorphism
1. The ascription of one's own characteristics to another.
1873H. Spencer Stud. Sociol. vi. 117 Our interpretations must be automorphic; and yet automorphism perpetually misleads us.
2. Math. (See quots.)
1903Science 5 June 904 Class of a group and degree of transitivity, automorphism, representation, index notation. 1955L. Mirsky Introd. Linear Algebra iv. 125 An automorphism of a linear manifold 𝔐 is an isomorphism of 𝔐 with itself. Ibid., A linear transformation of a finite-dimensional linear manifold onto itself is an automorphism. 1959M. Hall Theory of Groups vi. 86 The automorphism group A (C) is cyclic. 1959G. & R. C. James Math. Dict. 221/1 An isomorphism of a set with itself is an automorphism. An automorphism of a group is an inner automorphism if there is an element t such that x corresponds to x* if and only if x* = t-1 xt; it is an outer automorphism if it is not an inner automorphism. 1965J. J. Rotman Theory of Groups iv. 76 Definition. A homomorphism f:G → G is called an endomorphism of G; an isomorphism f:G → G is called an automorphism of G. |
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