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Abstract.
Let G be a group. An automorphism, α, of G is called fixed-point-free
if α fixes only the identity of G. We shall discuss some recent work of
Deaconescu and Walls regarding the structure of finite groups having a
certain kind of fixed-point-free automorphism. This work generalizes a
theorem of Burnside, which states that a finite group G admits a
fixed-point-free automorphism of order 2 if and only if G is abelian
and of odd order, by attempting to replace the order condition on α
with some other requirement.
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