Let G be a finite group, N(G) be the set of conjugacy classes of the group G. In the present paper it is proved, where G is a finite group with trivial center and L is a finite simple group of exceptional Lie type or Tits group.

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изоморфна унитарной или линейной группе степени 3 над некоторым ло-кально конечным полем характеристики 2. Мы обобщаем эти результаты. ТЕОРЕМА. Пусть периодическая группаПусть GF (q) конечное поле порядка q, SL 3 (q) = SL

One of the interesting classes of mixed groups ( i.e. groups that can contain both elements of finite order and elements of infinite order) is the class of Shunkov groups. The group $G$ is called Shunkov group if for any finite subgroup $H$ of $G$ in the quotient group $N_G(H)/H$, any two conjugate elements of prime order generate a finite group. When studying the Shunkov group $G$, a situation often arises when it is necessary to move to the quotient group of the group $G$ by some of its normal subgroup $N$. In which cases is the resulting quotient group $G/N$ again a Shunkov group? The paper gives a positive answer to this question, provided that the normal subgroup $N$ is locally finite and the orders of elements of the subgroup $N$ are mutually simple with the orders of elements of the quotient group $G/N$. Let $ \mathfrak{X}$ be a set of groups. A group $G$ is saturated with groups from the set $ \mathfrak{X}$ if any finite subgroup of $G$ is contained in a subgroup of $ G$ that is isomorphic to some group of $\mathfrak{X}$ . If all elements of finite orders from the group $G$ are contained in a periodic subgroup of the group $G$, then it is called the periodic part of the group $G$ and is denoted by $T(G)$. It is proved that the Shunkov group saturated with finite linear and unitary groups of degree 3 over finite fields has a periodic part that is isomorphic to either a linear or unitary group of degree 3 on a suitable locally finite field. \end{abstracte}

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