Is there a word that means "a group containing just 1 member?"

Question

Is there a word that can be used to describe a group or collection that only has 1 member/element? I first thought of singleton, but in my context singleton has a well-established meaning and I want to avoid confusion.

I want to ask a question like, "Does the group contain only one member?" with a more succinct, "Is the group a <insert-word-here>?" An analogous one would be: to ask if the group contains no elements, "Is the group empty?"

Put another way: empty is to "group with 0 elements" as <?> is to "group with 1 element."

"Bonus points" for a word that helps answer this more specific question succinctly: "Does the group contain only this one specific member?"

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Clarification: The "group" can have different number of elements at different times. Subsequently, in that context a "group" ("collection" if you prefer that word.; eg, a Set, List, Array, etc) can contain 0 or more elements and still be a valid "group")

Answer 1

Although 'unary', that is,

3. Composed of a single item or element.

OED Online

(alternatively defined here and here) is an adjective, it suits your desire for succinctness if the article is omitted: "Is the group unary?"

Answer 2

Singleton is used in computer programming (eg a class that can only have one instance) and in mathematics. For example, for a set containing only one element:

In mathematics, a singleton, also known as a unit set,1 is a set with exactly one element. For example, the set {0} is a singleton.

The term is also used for a 1-tuple (a sequence with one member).

Wikipedia

If the word singleton is unacceptable then maybe unit set, 1-tuple or unitary might be better. These all have their own existing meanings in computing and/or mathematics so might also cause confusion.

Answer 3

In American accounting, a type of business arrangement is the Limited Liability Company (LLC). An LLC can have several members or a single member. The Internal Revenue Service classifies an LLC with a lone member as a single-member LLC.

Answer 4

The succinct question could be phrased as "Is the the group an individual?", but that isn't exactly an answer for the broader question, since individual doesn't usually imply a group.

The usual phrasing (rather than being a single word) is "committee of one"