Abstract
The structure of finite groups is widely used in various fields and has a great influence on various disciplines. The object of this article is to classify these groups G whose number of elements of maximal order of G is 20.
Highlights
Finite groups are related in this article and our notation is standard
G always denotes a group, Sp denotes a Sylow p-subgroup of G, and A ∗ B denotes the center product of groups A and B
It is noted that G is solvable since the simple groups A5 and A6 have no element with order 12. us, (4.1) holds
Summary
Finite groups are related in this article and our notation is standard. G always denotes a group, Sp denotes a Sylow p-subgroup of G, and A ∗ B denotes the center product of groups A and B. If G satisfying M(G) 20 is A5-free, G is solvable
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