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Groups with an automorphism cubing many elements
Published online by Cambridge University Press: 09 April 2009
Extract
Let G be a group and αn the mapping which takes every element of G to its nth power, where n is an integer. It is well known that if αn is an automorphism then G is Abelian in the cases n = -1,2, and 3. For any other integer n(≠ 0) there exists a non-Abelian group which admits αn as the identity automorphism. Indeed Miller (1929) has shown that if n ≠ 0, ±1, 2, 3 then there exist non-Abelian groups which admit αn as a non-trivial automorphism.
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- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 20 , Issue 2 , September 1975 , pp. 253 - 256
- Copyright
- Copyright © Australian Mathematical Society 1975
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