Let \( G \) be a periodic group, and let \( \omega(G)\subseteq{𝕅} \) be the spectrum of \( G \) that is the set of orders of elements in \( G \). We prove that the alternating group \( A_{7} \) is uniquely recognized by its spectrum in the class of all groups.

中文翻译：

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通过其元素顺序集识别$ A_ {7} $

让\（G \）是周期性组，并且让\（\欧米加（G）\ subseteq {𝕅} \）是的频谱 \（G \） 是集合中的元素的顺序的 \（G \）。我们证明了交替组\（A_ {7} \）在所有组的类别中被其频谱唯一识别。