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Conjugate subgroups, normalizers and equivalent descriptions of crystal structures

Ulrich Müller

in Symmetry Relationships between Crystal Structures: Applications of Crystallographic Group Theory in Crystal Chemistry

Published in print:
2013
Published Online:
December 2013
ISBN:
9780199669950
eISBN:
9780191775086
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/acprof:oso/9780199669950.003.0008
Subject:
Physics, Crystallography: Physics, Condensed Matter Physics / Materials

Subgroups conjugate in a space group 𝒢 are subgroups that are equivalent by symmetry operations of 𝒢. This can be orientational or translational conjugation. The normalizer of a subgroup ℋ in the ... More


The Symmetry Group

Ercüment H. Ortaçgil

in An Alternative Approach to Lie Groups and Geometric Structures

Published in print:
2018
Published Online:
September 2018
ISBN:
9780198821656
eISBN:
9780191860959
Item type:
chapter
Publisher:
Oxford University Press
DOI:
10.1093/oso/9780198821656.003.0016
Subject:
Mathematics, Pure Mathematics

This chapter, which ends Part II on some consequences of the new approach, introduces an alternative prolongation theory of Klein geometries that is more geometric and intuitive than the well-known ... More


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