Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Geometric invariants for $p$-groups of class 2 and exponent $p$

E. A. O'Brien, Mima Stanojkovski

Abstract

We introduce geometric invariants for $p$-groups of class $2$ and exponent $p$. We report on their effectiveness in distinguishing among 5-generator $p$-groups of this type.

Geometric invariants for $p$-groups of class 2 and exponent $p$

Abstract

We introduce geometric invariants for -groups of class and exponent . We report on their effectiveness in distinguishing among 5-generator -groups of this type.

Paper Structure

This paper contains 11 sections, 4 theorems, 10 equations, 3 tables.

Table of Contents

  1. Introduction
  2. Geometric invariants associated to groups
  3. Groups from matrices and back
  4. Varieties and invariants
  5. An illustrative example
  6. The $5$-generator $p$-groups of class $2$ and exponent $p$
  7. Derived groups of order $p^3$
  8. Quasi-polynomiality
  9. Derived groups of order $p^4$
  10. Derived groups of order $p^5$
  11. Providing access to our results

Key Result

Lemma 2.1

Assume that $K=\mathbb{F}_p$ and write $G=\mathop{\mathrm{G}}\nolimits_{\mathop{\mathrm{B}}\nolimits}(\mathbb{F}_p)$.

Theorems & Definitions (7)

  • Lemma 2.1
  • Remark 2.2
  • Theorem 2.3
  • proof
  • Theorem 4.1
  • proof
  • Theorem 4.2