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math.GR2011★ 7 cited
Normal Subgroup Growth of Linear Groups: the (G2; F4;E8)-Theorem
Michael Larsen, Alexander Lubotzky
Let G be a finitely generated group and M_n(G) the number of its normal subgroup subgroups of index at most n. For linear groups G we show that M_n(G) can grow polynomially in n on…
math.GR2011
Waring Problem for Finite Quasisimple Groups
Michael Larsen, Aner Shalev, Pham Huu Tiep
The classical Waring problem deals with expressing every natural number as a sum of g(k) kth powers. Similar problems for finite simple groups have been studied recently, and in th…