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2. Embedding - Wikipedia

   en.wikipedia.org/wiki/Embedding

   In mathematics, an embedding (or imbedding [1]) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. When some object X {\displaystyle X} is said to be embedded in another object Y {\displaystyle Y} , the embedding is given by some injective and structure-preserving map f : X → ...

3. Word problem (mathematics) - Wikipedia

   en.wikipedia.org/wiki/Word_problem_(mathematics)

   In computational mathematics, a word problem is the problem of deciding whether two given expressions are equivalent with respect to a set of rewriting identities. A prototypical example is the word problem for groups , but there are many other instances as well.

4. Word problem (mathematics education) - Wikipedia

   en.wikipedia.org/wiki/Word_problem_(mathematics...

   Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

5. Word problem for groups - Wikipedia

   en.wikipedia.org/wiki/Word_problem_for_groups

   In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a finitely generated group is the algorithmic problem of deciding whether two words in the generators represent the same element of . The word problem is a well-known example of an undecidable problem.

6. SQ-universal group - Wikipedia

   en.wikipedia.org/wiki/SQ-universal_group

   Houcine has shown that the group F can be constructed so that it too has soluble word problem. This together with the fact that taking the direct product of two groups preserves solubility of the word problem shows that: The class of all finitely presented groups with soluble word problem is wrappable. Other examples of wrappable classes of ...

7. Subgroup distortion - Wikipedia

   en.wikipedia.org/wiki/Subgroup_distortion

   The simplification in a word problem induced by subgroup distortion suffices to construct a cryptosystem, algorithms for encoding and decoding secret messages. [4] Formally, the plaintext message is any object (such as text, images, or numbers) that can be encoded as a number n. The transmitter then encodes n as an element g ∈ H with word ...

8. List of undecidable problems - Wikipedia

   en.wikipedia.org/wiki/List_of_undecidable_problems

   Many, if not most, undecidable problems in mathematics can be posed as word problems: determining when two distinct strings of symbols (encoding some mathematical concept or object) represent the same object or not. For undecidability in axiomatic mathematics, see List of statements undecidable in ZFC.

9. Word problem - Wikipedia

   en.wikipedia.org/wiki/Word_problem

   Word problem (mathematics education), a type of textbook exercise or exam question to have students apply abstract mathematical concepts to real-world situations; Word problem (mathematics), a decision problem for algebraic identities in mathematics and computer science; Word problem for groups, the problem of recognizing the identity element ...