The Great Stellated 120-cell is one of the fascinating four-dimensional polytopes in the realm of higher-dimensional geometry. Specifically, it is one of the uniform 4-polytopes, and it belongs to the family of polytopes known as the stellar polytopes.

The icosahedral 120-cell, also known as the icosahedral honeycomb or 120-cell, is one of the six regular polytopes in four-dimensional space. It is a four-dimensional analog of the platonic solids and features a highly symmetric structure.

Yajnavalkya is a significant figure in ancient Indian philosophy and is best known as a sage and scholar in the tradition of Hinduism. He is often associated with the Brahmanas and Upanishads, particularly the "Brihadaranyaka Upanishad," which is one of the oldest Upanishads and a crucial text in the Vedanta philosophy.

A "range state" refers to a country or territory where a specific species of wildlife can be found. In conservation and environmental management contexts, the term is often used to denote the countries that are part of a species' natural range or distribution area. This is important for various regulatory and conservation efforts, especially for migratory species and those that may require international cooperation for their protection and management.

The small stellated 120-cell is a four-dimensional convex uniform polytope, which is an example of a 120-cell, a higher-dimensional analogue of a polyhedron in three dimensions. Specifically, this polytope is a member of the family of polytopes known as the "120-cells" or "120-vertex polytopes.

Abel's irreducibility theorem is a result in algebra that concerns the irreducibility of certain polynomials over the field of rational numbers (or more generally, over certain fields).

Prüfer's Theorem refers to a couple of important results in the context of graph theory, particularly regarding trees. Here are the two main aspects of Prüfer's Theorem often discussed: 1. **Prüfer Code (or Prüfer Sequence)**: The theorem states that there is a one-to-one correspondence between labeled trees with \( n \) vertices and sequences of length \( n-2 \) made up of labels from \( 1 \) to \( n \).

A Soroban is a traditional Japanese abacus used for performing arithmetic calculations. It consists of a rectangular frame with rods, each containing a number of movable beads. The Soroban typically has a unique structure: each rod contains one bead above a horizontal bar, which represents five units, and four beads below the bar, each representing one unit. The Soroban is used for addition, subtraction, multiplication, and division, and it is a highly effective tool for mental calculations and enhancing numerical skills.

In the context of abelian groups, the term "norm" can refer to a couple of different concepts depending on the specific field of mathematics being discussed. One common usage, particularly in algebra and number theory, is the notion of a norm associated with a field extension or a number field.

In the context of group theory, particularly in the study of abelian groups (and more generally, in the context of modules over a ring), the **torsion subgroup** is an important concept. The torsion subgroup of an abelian group \( G \) is defined as the set of elements in \( G \) that have finite order.

The Baer–Suzuki theorem is a result in group theory that deals with the structure of groups, specifically p-groups, and the conditions under which certain types of normal subgroups can be constructed. The theorem is part of a broader study in the representation of groups and the interplay between their normal subgroups and group actions.

The Carnot group is a specific type of mathematical structure found in the field of differential geometry and geometric analysis, often studied within the context of sub-Riemannian geometry and metric geometry. In particular, Carnot groups are a class of nilpotent Lie groups that can be understood in terms of their underlying algebraic structures.

The Freudenthal algebra, also known as the Freudenthal triple system, is a mathematical structure introduced by Hans Freudenthal in the context of nonlinear algebra. It is primarily used in the study of certain Lie algebras and has connections to exceptional Lie groups and projective geometry. A Freudenthal triple system is defined as a vector space \( V \) equipped with a bilinear product, which satisfies specific axioms.

Fitting's theorem, named after the mathematician W. Fitting, is a result in the field of group theory, specifically concerning the structure of finite groups. It provides important information about the composition of a finite group in terms of its normal subgroups and nilpotent components.

The Fontaine–Mazur conjecture is a significant conjecture in number theory, particularly in the areas of Galois representations and modular forms. Proposed by Pierre Fontaine and Bertrand Mazur in the 1990s, the conjecture relates to the solutions of certain Diophantine equations and the nature of Galois representations.

In ring theory, a branch of abstract algebra, the concept of "grade" often pertains to the structure of graded rings, which are rings that can be decomposed into a direct sum of abelian groups or modules indexed by integers or another grading set.

Grothendieck's connectedness theorem is a result in algebraic geometry that relates to the structure of schemes, particularly concerning the notion of connectedness in the context of the Zariski topology.

Petersson algebra, named after the mathematician Harold Petersson, is a specific algebraic structure that arises in the context of modular forms and number theory. It is particularly relevant in the study of modular forms of several variables and their associated spaces. In the context of modular forms, Petersson algebra describes the action of certain differential operators that provide a natural way to analyze and construct modular forms.

"Preradical" might refer to a concept or term that is not widely recognized in mainstream discourse as of my last training cut-off in October 2023. It could potentially be a term used in specific academic fields, niche discussions, or could be a typographical error or shorthand for something else, such as "pre-radical" in a political or ideological context.