## The monoid of semisimple multiclasses of the group $$G=G_2(K)$$.(Russian, English)Zbl 1052.20029

Zap. Nauchn. Semin. POMI 265, Pt. II, 202-221 (1999); translation in J. Math. Sci., New York 112, No. 4, 4355-4366 (2002).
A multiclass in a group $$G$$ is the product $$M=C_1\cdots C_k=\{c_1\cdots c_k\mid c_i\in C_i\}$$ of a finite sequence of conjugacy classes $$C_1,\dots,C_k\subset G$$. Let $$G$$ be a simple algebraic group and let $$M_{\text{cs}}(G)$$ denote the set of all closures (in the Zariski topology) of the multiclasses in $$G$$ generated by semisimple conjugacy classes. $$M_{\text{cs}}(G)$$ is a commutative monoid with respect to the operation $$m_1m_2=\overline{m_1m_2}$$, where $$\overline m$$ is the closure of $$m$$. N. L. Gordeev [J. Algebra 173, No. 3, 715-744 (1995; Zbl 0832.14037)] described the structure of the monoid $$M_{\text{cs}}(G)$$ for the group $$G=\text{SL}_n(K)$$, where $$K$$ is an algebraically closed field of characteristic zero. In this paper the structure of $$M_{\text{cs}}(G)$$ is described for the case $$G=G_2(K)$$.

### MSC:

 20G15 Linear algebraic groups over arbitrary fields 20E45 Conjugacy classes for groups

Zbl 0832.14037
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