The authors introduce and study the class of groups graded by root systems. They prove that if is an irreducible classical root system of rank and is a group graded by , then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of . As the main application of this theorem the authors prove that for any reduced irreducible classical root system of rank and a finitely generated commutative ring with , the Steinberg group and the elementary Chevalley group have property . They also show that there exists a group with property which maps onto all finite simple groups of Lie type and rank , thereby providing a “unified” proof of expansion in these groups.
Linking neoliberalism with the Right’s global rise Bulgaria’s media-driven pivot to right-wing populism parallels political developments taking place around the world. Martin Marinos applies a critical political economy approach to place Bulgarian right-wing populism within the structural transformation of the country’s media institutions. As Marinos shows, media concentration under Western giants like Westdeutsche Allgemeine Zeitung and News Corporation have led to a neoliberal turn of commercialization, concentration, and tabloidization across media. The Right have used the anticommunism and racism bred by this environment to not only undermine traditional media but position their own outlets to boost new political entities like the nationalist party Ataka. Marinos’s ethnographic observations and interviews with local journalists, politicians, and media experts add on-the-ground detail to his account. He also examines several related issues, including the performative appeal of populist media and the money behind it. A timely and innovative analysis, Free to Hate reveals where structural changes in media intersect with right-wing populism.
The authors introduce and study the class of groups graded by root systems. They prove that if is an irreducible classical root system of rank and is a group graded by , then under certain natural conditions on the grading, the union of the root subgroups is a Kazhdan subset of . As the main application of this theorem the authors prove that for any reduced irreducible classical root system of rank and a finitely generated commutative ring with , the Steinberg group and the elementary Chevalley group have property . They also show that there exists a group with property which maps onto all finite simple groups of Lie type and rank , thereby providing a “unified” proof of expansion in these groups.
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