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A class of polynomial permutations on groups

Part of: Permutation groups

Published online by Cambridge University Press:  09 April 2009

G. Kowol
G. Kowol
Affiliation:
University of Vienna1090 Vienna, Austria
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Abstract

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Let G be a finite and u(G) the group of all invertible transformations (polynomial permutations) of the form x→a1 x1→ xk a2⃛ar xkr ar+1 (aiε G, x runs through G). Continuing investigations of H. Lausch of groups satisfying u(G) = {X→axk b} we show here that this condition implies that G is the direct product of its {2, 3}-Hall subgroup and its {2, 3}′-Hall subgroup H where H is nilpoint of class ≤2. Essentially all non-nilpoint groups G of order 2m 3n are described having the property u(G)= {x→axk b}

MSC classification

Secondary: 20B99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 2 , March 1979 , pp. 189 - 198
Copyright
Copyright © Australian Mathematical Society 1979

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