Sentence examples for trivial group from inspiring English sources

To paraphrase: if the letters of the alphabet are a group (in the strict mathematical sense) then this group is the "trivial group" in which every element is equal to 1.

If any two different-meaning words which sound the same are "equivalent" we shall show each letter of the alphabet (as well as space and apostrophe) generates the trivial group, i.e. all alphabet letters (and space and apostrophe) equal the identity element.

Thus G × 0 is just the trivial group { e }.

Then, for all q > m, C q κ ( X ) is a trivial group.

Then if q > m, then C q κ ( X ) is a trivial group.

Please note that this includes even the case of the trivial group (K = mathrm {SO}_1 = { mathrm {Id} }) with any (p = q > 0,).

Supposedly some non-trivial group of people fail at simple exercises like FizzBuzz.

Part of the difficulty emerges from the fact that the logical consequences of a non-trivial group of axioms are often not transparent: significant work is required to establish such consequences.

It is shown that, for a non-trivial group G, each normal edge transitive Cayley graph for G has at least one homomorphic image which is a normal edge transitive Cayley graph for a characteristically simple quotient group of G.

In order to maintain good functional specificity for shared functions, without reducing the population of the resulting groups to a trivial number, groups were defined by the lowest internal node that achieved the minimum size threshold.

With films made for sums that are, in Hollywood terms, trivial, this group and others established a new standard of quality, originality, and authenticity.