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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

The group of automorphisms of a class of finite $ p$-groups


Author: Arye Juhász
Journal: Trans. Amer. Math. Soc. 270 (1982), 469-481
MSC: Primary 20D45
DOI: https://doi.org/10.1090/S0002-9947-1982-0645325-3
MathSciNet review: 645325
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Abstract: Let $ G$ be a finite $ p$-group and denote by $ {K_i}(G)$ the members of the lower central series of $ G$. We call $ G$ of type $ (m,\,n)$ if (a) $ G$ has nilpotency class $ m - 1$, (b) $ G/{K_2}(G) \cong {{\mathbf{Z}}_{{p^n}}} \times {{\mathbf{Z}}_{{p^n}}}$ and $ {K_i}(G)/{K_{i + 1}}(G) \cong {{\mathbf{Z}}_{{p^n}}}$ for every $ i$, $ 2 \leqslant i \leqslant n - 1$. In this work we describe the structure of $ \operatorname{Aut} (G)$ and certain relations between $ \operatorname{Out} (G)$ and $ G$.


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DOI: https://doi.org/10.1090/S0002-9947-1982-0645325-3
Keywords: Finite $ p$-group, automorphism group, metabelian group, power-structure of $ p$-groups, commutator-structure of $ p$-groups, $ p$-groups of maximal class
Article copyright: © Copyright 1982 American Mathematical Society