TL;DR
This paper investigates the properties of Singer's fifth algebraic transfer, demonstrating that it is not an epimorphism in degree 11 and does not detect a specific element in the Ext algebra.
Contribution
It provides a counterexample showing that Singer's fifth transfer fails to be surjective in a particular degree, clarifying its limitations.
Findings
Singer's fifth transfer is not an epimorphism in degree 11.
It does not detect the element P(h_2) in Ext_A^{5,16}(F_2,F_2).
The result refines understanding of algebraic transfer behavior.
Abstract
In this paper, we show that Singer's fifth transfer is not an epimorphism in degree 11. More precisely, it does not detect the element P(h_2) in Ext_A^{5,16}(F_2,F_2).
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