Reality properties of conjugacy classes in algebraic groups
نویسندگان
چکیده
منابع مشابه
Reality Properties of Conjugacy Classes in Algebraic Groups
Let G be an algebraic group defined over a field k. We call g ∈ G real if g is conjugate to g−1 and g ∈ G(k) as k-real if g is real in G(k). An element g ∈ G is strongly real if ∃h ∈ G, h2 = 1 (i.e. h is an involution) such that hgh−1 = g−1. Clearly, strongly real elements are real and are product of two involutions. Let G be a connected adjoint semisimple group over a perfect field k, with −1 ...
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We prove the Arad–Herzog conjecture for various families of finite simple groups — if A and B are nontrivial conjugacy classes, then AB is not a conjugacy class. We also prove that if G is a finite simple group of Lie type and A and B are nontrivial conjugacy classes, either both semisimple or both unipotent, then AB is not a conjugacy class. We also prove a strong version of the Arad–Herzog co...
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Suppose $G$ is a finite group, $A$ and $B$ are conjugacy classes of $G$ and $eta(AB)$ denotes the number of conjugacy classes contained in $AB$. The set of all $eta(AB)$ such that $A, B$ run over conjugacy classes of $G$ is denoted by $eta(G)$.The aim of this paper is to compute $eta(G)$, $G in { D_{2n}, T_{4n}, U_{6n}, V_{8n}, SD_{8n}}$ or $G$ is a decomposable group of order $2pq$, a group of...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2008
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-008-1001-6