The difference between Group and Monoid

When used as nouns, group means a number of things or persons being in some relation to one another, whereas monoid means a set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.

Group is also verb with the meaning: to put together to form a group.

Monoid is also adjective with the meaning: containing only one kind of metrical foot.

check bellow for the other definitions of Group and Monoid

  1. Group as a noun:

    A number of things or persons being in some relation to one another.

    Examples:

    "there is a group of houses behind the hill; he left town to join a Communist group'"

    "A group of people gathered in front of the Parliament to demonstrate against the Prime Minister's proposals."

  2. Group as a noun (group theory):

    A set with an associative binary operation, under which there exists an identity element, and such that each element has an inverse.

  3. Group as a noun (geometry, archaic):

    An effective divisor on a curve.

  4. Group as a noun:

    A (usually small) group of people who perform music together.

    Examples:

    "Did you see the new jazz group?"

  5. Group as a noun (astronomy):

    A small number (up to about fifty) of galaxies that are near each other.

  6. Group as a noun (chemistry):

    A column in the periodic table of chemical elements.

  7. Group as a noun (chemistry):

    A functional group.

    Examples:

    "Nitro is an electron-withdrawing group."

  8. Group as a noun (sociology):

    A subset of a culture or of a society.

  9. Group as a noun (military):

    An air force formation.

  10. Group as a noun (geology):

    A collection of formations or rock strata.

  11. Group as a noun (computing):

    A number of users with same rights with respect to accession, modification, and execution of files, computers and peripherals.

  12. Group as a noun:

    An element of an espresso machine from which hot water pours into the portafilter.

  13. Group as a noun (music):

    A number of eighth, sixteenth, etc., notes joined at the stems; sometimes rather indefinitely applied to any ornament made up of a few short notes.

  14. Group as a noun (sports):

    A set of teams playing each other in the same division, while not during the same period playing any teams that belong to other sets in the division.

  15. Group as a noun (business):

    A commercial organization.

  1. Group as a verb (transitive):

    To put together to form a group.

    Examples:

    "group the dogs by hair colour"

  2. Group as a verb (intransitive):

    To come together to form a group.

  1. Monoid as a noun (mathematics):

    A set which is closed under an associative binary operation, and which contains an element which is an identity for the operation.

  1. Monoid as an adjective (prosody):

    Containing only one kind of metrical foot.

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