Space groups, subgroups and a lot more

Equivalence among isotropy subgroups of space groups.

The Landau theory' of continuous phase transitions provides a powerful tool for understanding transitions between solid phases whose symmetries have a group-subgroup relationship. In the Landau theory, the thermodynamic free energy F of the crystal is written as a function of an order parameter Q. In the high-symmetry phase, the minimum of F is at Q = 0. In the low-symmetry phase, the minimum o...

Computing Maximal Subgroups and Wyckoff Positions of Space Groups

This paper describes algorithms for the computation of conjugacy classes of maximal subgroups and the Wyckoo positions of a space group. The algorithms are implemented in the computational group theory system GAP and use existing standard functions of GAP as well as some simple but useful group theoretical ideas. Synopsis: Algorithms for the computation of maximal subgroups and Wyckoo positions...

More on lot-to-lot changes.

POS-groups with some cyclic Sylow subgroups

A finite group G is said to be a POS-group if for each x in G the cardinality of the set {y in G | o(y) = o(x)} is a divisor of the order of G. In this paper we study the structure of POS-groups with some cyclic Sylow subgroups.

Practical algorithm for identifying subgroups of space groups.

is considered. The properties of space groups and subgroups are given in terms of an algebraic rather than a geometric description. In this algebraic description, 6 is equivalent to one of the standard listings through a similarity transformation consisting of a linear unimodular component and a translation. A general algorithm is presented to determine which standard listing corresponds to sub...