中文摘要：

单群L4（4）,L4（7）,U4（5）,U4（7）素图分量为1,施武杰、V.D.Mazurov教授的公开问题中交错群A22的素图分量为1的单群,是否为用元素阶的集合可刻画的群？本文就素图分量为1的单群L4（4）得到如下定理：设G为有限群,则G L4（4）,当且仅当πe（G）=πe（L4（4））.

英文摘要：

W.J.Shi and V.D.Mazurov put forward an open problem：Is alternating group A22 recognizable by their element orders？ Because of these groups with connected Gruenberg Kegel graph,the problem is a difficult one.What about L4（4）,L4（7）,U4（5）,U4（7） with connected Gruenberg Kegel graph？In this paper it is shown that L4（4） is recognizable by its element orders.