Totally Zippin $p$-groups
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- by Charles Megibben PDF
- Proc. Amer. Math. Soc. 91 (1984), 15-18 Request permission
Abstract:
If $G$ is a $p$-group of limit length $\lambda$, then it satisfies the $\lambda$-Zippin property provided that whenever $A/{p^\lambda }A \cong G \cong B/{p^\lambda }B$, every isomorphism between ${p^\lambda }A$ and ${p^\lambda }B$ extends to an isomorphism between $A$ and $B$. We show that if $G$ is almost balanced in a totally projective group, then $G$ does satisfy the $\lambda$-Zippin property. This leads to the existence of a great variety of $G$โs that are totally Zippin in the sense that $G/{p^\alpha }G$ satisfies the $\alpha$-Zippin property for all limit ordinals $\alpha \leqslant \lambda = {\text {length of }}G$. Hence totally Zippin $p$-groups need not be $S$-groups, although those of countable length turn out to be direct sums of countable groups.References
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Additional Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 91 (1984), 15-18
- MSC: Primary 20K10; Secondary 20K25, 20K35, 20K40
- DOI: https://doi.org/10.1090/S0002-9939-1984-0735555-1
- MathSciNet review: 735555