We prove various properties on the structure of groups whose power graph is chordal. Nilpotent groups with this property have been classified by (Electron J Combin 28(3):14, 2021). Here we classify the finite simple groups with chordal power graph, relative to typical number theoretic conditions. We do so by devising several sufficient conditions for the existence and non-existence of long cycles in power graphs of finite groups. We examine other natural group classes, including special linear, symmetric, generalized dihedral and quaternion groups, and we characterize direct products with chordal power graph. The classification problem is thereby reduced to directly indecomposable groups, and we further obtain a list of possible socles. Lastly, we give a general bound on the length of an induced path in chordal power graphs, providing another potential road to advance the classification beyond simple groups.

我们证明了幂图为弦的群结构的各种性质。具有此性质的幂零群已按 (Electron J Combin 28(3):14, 2021) 进行分类。在这里，我们相对于典型的数论条件，用弦幂图对有限单群进行分类。我们通过设计有限群幂图中存在和不存在长循环的几个充分条件来做到这一点。我们研究其他自然群类，包括特殊线性群、对称群、广义二面体群和四元数群，并用弦幂图来表征直积。由此，分类问题被简化为直接不可分解的群，并且我们进一步获得了可能的基础列表。最后，我们给出了弦功率图中感应路径长度的一般界限，