**Definitions**

A group *G* is called *boundedly generated* if there exists a finite subset *S* of *G* and a positive integer *m* such that every element *g* of *G* can be represented as a product of at most *m* powers of the elements of *S*:

- where and are integers.

The finite set *S* generates *G*, so a boundedly generated group is finitely generated.

An equivalent definition can be given in terms of cyclic subgroups. A group *G* is called *boundedly generated* if there is a finite family *C*_{1}, …, *C*_{M} of not necessarily distinct cyclic subgroups such that *G* = *C*_{1}…*C*_{M} as a set.

Read more about this topic: Boundedly Generated Group

### Other articles related to "definitions, definition":

... that cannot be confused with other words or

**definitions**... He gave emphasis on avoidance of words that have many

**definitions**and compared the language of Scientology with the language of Math and other precise doctrines ... a heavy emphasis on understanding word

**definitions**...

**Definitions**- South America

... Although topographic maps of the Chile and Argentina border region which contains the highest peaks are of notoriously poor accuracy, with elevation errors exceeding 100 metres (330 ft) in many cases, the current consensus based on the most recent measurements places Ojos del Salado as the 2nd highest peak and highest volcano in South America, significantly higher than Monte Pissis. ...

... A theoretical (or conceptual)

**definition**gives the meaning of a word in terms of the theories of a specific discipline ... This type of

**definition**assumes both knowledge and acceptance of the theories that it depends on ... An example of a theoretical

**definition**is that of "Heat" in physics, which actually puts forth an entire theory of heat (involving accelerating molecules, etc.) ...

... Some

**definitions**of language, such as early versions of Charles Hockett's "design features"

**definition**, emphasize the spoken nature of language ... Mathematics would not qualify as a language under these

**definitions**, as it is primarily a written form of communication (to see why, try reading Maxwell's equations out loud) ... However, these

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### Famous quotes containing the word definitions:

“What I do not like about our *definitions* of genius is that there is in them nothing of the day of judgment, nothing of resounding through eternity and nothing of the footsteps of the Almighty.”

—G.C. (Georg Christoph)

“The loosening, for some people, of rigid role *definitions* for men and women has shown that dads can be great at calming babies—if they take the time and make the effort to learn how. It’s that time and effort that not only teaches the dad how to calm the babies, but also turns him into a parent, just as the time and effort the mother puts into the babies turns her into a parent.”

—Pamela Patrick Novotny (20th century)

“Lord Byron is an exceedingly interesting person, and as such is it not to be regretted that he is a slave to the vilest and most vulgar prejudices, and as mad as the winds?

There have been many *definitions* of beauty in art. What is it? Beauty is what the untrained eyes consider abominable.”

—Edmond De Goncourt (1822–1896)