Large $${\varvec{p}}^{\prime }$$-orbits for $${\varvec{p}}$$p-nilpotent linear groups |
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Authors: | Email author" target="_blank">David?GluckEmail author |
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Institution: | 1.Department of Mathematics,Wayne State University,Detroit,USA |
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Abstract: | Let G be a p-nilpotent linear group on a finite vector space V of characteristic p. Suppose that |G||V| is odd. Let P be a Sylow p-subgroup of G. We show that there exist vectors \(v_1\) and \(v_2\) in V such that \(C_G(v_1) \cap C_G(v_2)=P\). A striking conjecture of Malle and Navarro offers a simple global criterion for the nilpotence (in the sense of Broué and Puig) of a p-block of a finite group. Our result implies that this conjecture holds for groups of odd order. |
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