Abstract Additivity with respect to exact sequences is, notoriously, a fundamental property of the algebraic entropy of group endomorphisms. It was proved for abelian groups by using the structure theorems for such groups in an essential way. On the other hand, a solvable counterexample was recently found, showing that it does not hold in general. Nevertheless, we give a rather short proof of the additivity of algebraic entropy for locally finite groups that are either quasihamiltonian or FC-groups.

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具有可置换有限子群的局部有限群的代数熵的可加性

摘要 众所周知，关于精确序列的可加性是群自同态的代数熵的基本​​性质。对阿贝尔群使用结构定理在本质上证明了这种群。另一方面，最近发现了一个可解的反例，表明它一般不成立。尽管如此，我们还是给出了一个相当简短的证明，证明了局部有限群的代数熵的可加性，这些群要么是拟哈密尔顿群，要么是 FC 群。