On double centralizer subgroups of some finite $p$-groups
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- by Ying Cheng PDF
- Proc. Amer. Math. Soc. 86 (1982), 205-208 Request permission
Abstract:
Let $A$ be a maximal abelian normal subgroup of a finite $p$-group $G(p > 2)$ such that $[G,A]$ is cyclic. Then (i) ${C_G}({C_G}(D)) = D$ and $[G:{C_G}(D)] = [D:Z(G)]$ for every $Z(G) \leqslant D \leqslant G$; (ii) $[G:Z(G)] = {[G,A]^2}$ and every faithful absolutely irreducible representation of $G$ is of degree $[G:A]$. The case $p = 2$ will also be mentioned.References
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Y. Cheng, On finite $p$-groups with cyclic commutator subgroup, Arch. Math. (to appear).
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 86 (1982), 205-208
- MSC: Primary 20D15
- DOI: https://doi.org/10.1090/S0002-9939-1982-0667273-0
- MathSciNet review: 667273