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We prove that groups definable in o-minimal structures have Cartan subgroups, and only finitely many conjugacy classes of such subgroups. We also delineate with precision how these subgroups cover the ambient group, in general very largely in terms of the dimension.
In this paper we completely characterize solvable real Lie groups definable in o-minimal expansions of the real field.
In this paper, we show that all Coleman automorphisms of a finite group with self-central minimal non-trivial characteristic subgroup are inner; therefore the normalizer property holds for these groups. Using our methods we show that the holomorph an
Let $pi$ be a set of primes. According to H. Wielandt, a subgroup $H$ of a finite group $X$ is called a $pi$-submaximal subgroup if there is a monomorphism $phi:Xrightarrow Y$ into a finite group $Y$ such that $X^phi$ is subnormal in $Y$ and $H^phi=K
Recent results of Qu and Tuarnauceanu describe explicitly the finite p-groups which are not elementary abelian and have the property that the number of their subgroups is maximal among p-groups of a given order. We complement these results from the b
Following Isaacs (see [Isa08, p. 94]), we call a normal subgroup N of a finite group G large, if $C_G(N) leq N$, so that N has bounded index in G. Our principal aim here is to establish some general results for systematically producing large subgroup