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A normal form for a group G with generating set S is a choice of one reduced word in S for each element of G. For example: For example: The words 1, i , j , ij are a normal form for the Klein four-group with S = { i , j } and 1 representing the empty word (the identity element for the group).
A free group has a unique normal form i.e. each element in is represented by a unique reduced word. Proof. An elementary transformation of a word w ∈ G {\displaystyle w\in G} consists of inserting or deleting a part of the form a a − 1 {\displaystyle aa^{-1}} with a ∈ S ± {\displaystyle a\in S^{\pm }} .
Tests for constituents are diagnostics used to identify sentence structure. There are numerous tests for constituents that are commonly used to identify the constituents of English sentences. 15 of the most commonly used tests are listed next: 1) coordination (conjunction), 2) pro-form substitution (replacement), 3) topicalization (fronting), 4) do-so-substitution, 5) one-substitution, 6 ...
In linguistics, a consonant cluster, consonant sequence or consonant compound, is a group of consonants which have no intervening vowel. In English, for example, the groups /spl/ and /ts/ are consonant clusters in the word splits. In the education field it is variously called a consonant cluster or a consonant blend. [1] [2]
The free abelian group on S can be explicitly identified as the free group F(S) modulo the subgroup generated by its commutators, [F(S), F(S)], i.e. its abelianisation. In other words, the free abelian group on S is the set of words that are distinguished only up to the order of letters. The rank of a free group can therefore also be defined as ...
As such, primary groups or lack thereof [citation needed] play an important role in the development of personal identity, and can be understood as tight circles composed of people such as family, long-term romances, crisis-support group, church group, etc. [4] The concept of the primary group was first introduced in 1909 by sociologist Charles ...
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The Sursurunga greater paucal is used for groups of four or more (and must be used instead of the plural for a group of two or more dyads). There is thus some overlap between the two groups; a family of four can be referred to in Sursurunga by either of the paucals. [119]