Identity theorem for pro-$p$-groups

Abstract

We prove the Identity Theorem for pro-$p$-groups with a single defining relation giving a positive feedback to a question of Serre on the structure of relation modules. A construction of "conjurings" indicates finality of our result in a certain sense.

Comparing to previous versions several changes are made (now in English), proofs are expanded and corrected. Comments are welcome!

References in corpus (4)

• Proalgebraic crossed modules of quasirational presentations
• Quasirational relation modules and p-adic Malcev completions
• Quasirationality and aspherical (pro-$p$)presentations
• Comparison of the Discrete and Continuous Cohomology Groups of a Pro-$p$ Group

Cited by in corpus (3)

• Proalgebraic crossed modules of quasirational presentations
• Quasirationality and prounipotent crossed modules
• Rational and $p$-adic analogs of J.H.C. Whitehead's conjecture