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Explicit inverse Shapiro isomorphism and its application

Andrei V. Zavarnitsine

Abstract

We find an explicit form of the inverse isomorphism from Shapiro's lemma in terms of inhomogeneous cocycles and apply it to construct special nonsplit coverings of groups with a unique conjugacy class of involutions.

Explicit inverse Shapiro isomorphism and its application

Abstract

We find an explicit form of the inverse isomorphism from Shapiro's lemma in terms of inhomogeneous cocycles and apply it to construct special nonsplit coverings of groups with a unique conjugacy class of involutions.

Paper Structure

This paper contains 6 sections, 8 theorems, 62 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Inhomogeneous resolution
  4. Homotopy of resolutions for a subgroup
  5. Main proof
  6. An application

Key Result

Theorem 1

In the above notation, the inverse Shapiro isomorphism $\Theta^{-1}$ is induced from the map on inhomogeneous cocycles for every $\beta\in Z^n(H,U)$ and $g_1,\ldots,g_{n+1}\in G$, where the elements $h_i\in H$ are uniquely determined from the relations for $i=1,\ldots,n+1$.

Theorems & Definitions (12)

  • Theorem 1
  • Proposition 2
  • Lemma 3
  • Lemma 4
  • Lemma 5
  • proof
  • Proposition 6
  • proof
  • Lemma 7
  • proof
  • ...and 2 more