The editorial preparation of Volume A1 has been completed and its LaTeX-based files are now being processed by the office of the Technical Editor in Chester. This update to the Volume A1 page contains a very brief description and a complete Table of Contents of the volume. It is expected that Volume A1 will be published within the year 2004.

The main topics of this volume are group-subgroup relations between space groups, and relations between the Wyckoff positions of the space groups and their subgroups. The presentation of these topics is preceded by a historical introduction and helpful explanatory matter. The data have been generated by computer, and instructions for their regeneration by the reader are also included.

As of the date of the present update, the technical editing of Volume A1 has been essentially completed. Final proofreading is now underway. Volume A1 is expected to appear within the second half of 2004, as planned.

**CONTENTS OF VOLUME A1**

**Foreword**

**Scope of this Volume (by M.I. Aroyo, U. Müller and H. Wondratschek)**

**Computer production of Parts 2 and 3 (by P. Konstantinov, A. Kirov, E.B.
Kroumova, M.I. Aroyo and U. Müller)**

**List of symbols and abbreviations**

**PART 1. SPACE GROUPS AND THEIR SUBGROUPS**

**1.1. Historical introduction (by M.I. Aroyo, U. Müller and H. Wondratschek)**- 1.1.1. The fundamental laws of crystallography
- 1.1.2. Symmetry and crystal-structure determination
- 1.1.3. Development of the theory of group-subgroup relations
- 1.1.4. Applications of group-subgroup relationships
**1.2. General introduction to subgroups of space groups (by H. Wondratschek)**- 1.2.1. General remarks
- 1.2.2. Mappings and matrices
- 1.2.3. Groups
- 1.2.4. Subgroups
- 1.2.5. Space groups
- 1.2.6. Types of subgroups of space groups
- 1.2.7. Application to domain structures
- 1.2.8. Lemmata on subgroups of space groups
**1.3. Remarks on Wyckoff positions (by U. Müller)**- 1.3.1. Introduction
- 1.3.2. Crystallographic orbits and Wyckoff positions
- 1.3.3. Derivative structures and phase transitions
- 1.3.4. Relationships between the positions in group-subgroup relations
**1.4. Computer checking of the subgroup data (by F. Gähler)**- 1.4.1. Introduction
- 1.4.2. Basic capabilities of the `Cryst' package
- 1.4.3. Computing maximal subgroups
- 1.4.4. Description of the checks
**1.5. Mathematical background of the subgroup tables (by G. Nebe)**- 1.5.1. Introduction
- 1.5.2. The affine space
- 1.5.3. Groups
- 1.5.4. Space groups
- 1.5.5. Maximal subgroups
- 1.5.6. Quantitative results
- 1.5.7. Qualitative results

**PART 2. MAXIMAL SUBGROUPS OF THE PLANE GROUPS AND SPACE GROUPS**

- 2.1.1. Contents and arrangement of the subgroup tables
- 2.1.2. Structure of the subgroup tables
- 2.1.3. I Maximal
*translationengleiche*subgroups (*t*-subgroups) - 2.1.4. II Maximal
*klassengleiche*subgroups (*k*-subgroups) - 2.1.5. Series of maximal isomorphic subgroups (by Y. Billiet)
- 2.1.6. Minimal supergroups
- 2.1.7. The subgroup graphs

**PART 3. RELATIONSHIPS BETWEEN THE WYCKOFF POSITIONS**

**3.1. Guide to the tables (by U. Müller)**- 3.1.1. Arrangement of the entries
- 3.1.2. Cell transformations
- 3.1.3. Origin shifts
- 3.1.4. Non-conventional settings of orthorhombic space groups
- 3.1.5. Conjugate subgroups
- 3.1.6. Monoclinic and triclinic subgroups
**3.2. Tables of the relationships of the Wyckoff positions (by U. Müller)**

**Appendix: Differences in the presentation in Parts 2 and 3 (by U. Müller and H. Wondratschek)**

**References**

**Subject index**

Updated 22 March 2004

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