科研之友
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摘要
Let G be a finite group of order n, and let C-n be the cyclic group of order n. For g is an element of G, let o(g) denote the order of g. Let phi denote the Euler totient function. We show that Sigma(g is an element of Cn) phi(o(g)) %26gt;= Sigma(g is an element of G) phi(o(g)), with equality if and only if G is isomorphic to Cn. As an application, we show that among all finite groups of a given order, the cyclic group of that order has the maximum number of bidirectional edges in its directed power graph.
- 出版日期2014-12
