Boolean代数上的一个置换群

A Permutation Group on Boolean Algebra

本文在[1]的基础上得到如下结果:定理1,是一个Abelian群;定理2,若,则。

In paper [1], it is showed that a Boolean algebra (B, ∧_1, ∨_1) is obtained by the mapping φa:al→(a∧u')∨(a'∧u) from(B, ∧, ∨) noto(B, ∧_1, ∨_1), and the two Boolean algebras are isomorphic. The present paper obtanis the following results: Theorem 1. A= { φ_u丨u∈B} is an abelian group. Theorem 2. If B_1≌ B_2, then A_B_1 ={φu∈B_1{≌A_B_2={φ_u丨v∈B_2}.