| 释义 |
self-ˈconjugate, a. Math.
[self- 3 a.]
a. Applied to a figure each side of which is, relatively to some conic, the polar of the opposite vertex. Of a function (see quot. 1873). Hence self-conjugation, the state of being self-conjugate.
1866Hamilton Quaternions §349 Where the function ϕορ is its own conjugate, or is the common self-conjugate part of ϕρ and ϕ′ρ. Ibid. §353 When this condition of self-conjugation is not satisfied. 1873Maxwell Electr. & Magn. I. 12 In Quaternion language, the one vector is said to be a linear and vector function of the other, and when there are three pairs of equal coefficients the function is said to be self-conjugate. 1885J. Casey Analyt. Geom. 305 Let the conics be referred to their common self-conjugate triangle. 1893in Cayley Math. Papers (1897) XIII. 269 Of course, here a self-conjugate term such as bcd is put in evidence.
b. Of a subgroup: having the property that for any elements h in the subgroup and g in the group, the product ghg-1 is in the subgroup.
1888G. G. Morrice tr. Klein's Lectures on Ikosahedron i. i. 7 Every group contains..two self-conjugate subgroups: viz., in the first place, the totality of all its operations, i.e., the group itself, and, in the second place, that simplest group which consists of the identical operation alone. 1937A. A. Albert Mod. Higher Algebra vi. 131 We call ℌ a normal divisor (or invariant subgroup, or self-conjugate subgroup) of 𝔊. 1979Page & Wilson Introd. Computational Combinatorics iv. 74 A partition whose Ferrers graph reads the same by rows and by columns is called self-conjugate.
Hence self-ˈconjugately adv., as a self-conjugate subgroup.
1897W. Burnside Theory of Groups x. 208 If two of these sub-groups have a common subgroup of order 4, it must be contained self-conjugately..in a sub-group of order 24 or 56. 1901L. E. Dickson Linear Groups p. vii, Largest subgroup containing the Abelian group self-conjugately. |