Groups with Anticentral Elements |
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| Authors: | Frieder Ladisch |
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| Institution: | 1. Mathematics Institute , University of Rostock , Rostock, Germany frieder.ladisch@uni-rostock.de |
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| Abstract: | We study finite groups G with elements g such that |C G (g)| = |G:G′|. (Such elements generalize fixed-point-free automorphisms of finite groups.) We show that these groups have a unique conjugacy class of nilpotent supplements for the commutator subgroup and, using the classification of finite simple groups, that these groups are solvable. |
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| Keywords: | Carter subgroup Centralizers Finite groups Solvable groups |
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