Sylow 2-subgroups of solvable Q-groups.
A finite group whose irreducible characters are rational valued is called a rational or a Q-group. In this paper we obtain various results concerning the structure of a Sylow 2-subgroup of a solvable Q-group.
Some results on -groups
Some results on the recognizability of the linear groups over the binary field
In this paper, we first find the set of orders of all elements in some special linear groups over the binary field. Then, we will prove the characterizability of the special linear group using only the set of its element orders.
A characterization property of the simple group by the set of its element orders
Let denote the set of element orders of a finite group . If is a finite non-abelian simple group and implies contains a unique non-abelian composition factor isomorphic to , then is called quasirecognizable by the set of its element orders. In this paper we will prove that the group is quasirecognizable.
A characterization of the simple group by the set of its element orders.
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