der Ring
ring
A piece of jewelry that you wear on your finger.
Zur Verlobung hat er ihr einen goldenen Ring geschenkt.
For their engagement, he gave her a gold ring.

ring
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ring
A piece of jewelry that you wear on your finger.
Zur Verlobung hat er ihr einen goldenen Ring geschenkt.
For their engagement, he gave her a gold ring.

As a piece of jewelry, 'Ring' (ring) is often used with the verbs 'tragen' (to wear) or 'anstecken' (to put on). Common compounds are 'Ehering' (wedding ring) and 'Verlobungsring' (engagement ring).
Sie trägt einen wunderschönen Ring mit einem blauen Stein am Finger.
She is wearing a beautiful ring with a blue stone on her finger.
When referring to a group of people, the preposition 'im' is often used. Typical verbs are 'im Ring sitzen' (to sit in a ring) or 'im Ring stehen' (to stand in a ring).
Die Kinder standen im Ring und spielten ein Spiel.
The children stood in a ring and played a game.
In the context of traffic and city maps, 'Ring' (ring road) refers to a road that runs around the center. Here the preposition 'auf' is used, for example 'auf dem Ring fahren' (to drive on the ring road).
Auf dem Mittleren Ring gibt es momentan viel Stau.
There is currently a lot of traffic on the Mittlerer Ring.
In boxing, the preposition is important. 'In den Ring steigen' (to step into the ring) with the accusative describes movement. 'Im Ring kämpfen' (to fight in the ring) with the dative describes position.
Der Herausforderer steigt selbstbewusst in den Ring.
The challenger steps confidently into the ring.
When the topic is crime, 'Ring' (ring) refers to an illegal organization. Signal words are verbs like 'zerschlagen' (to break up) or 'ausheben' (to bust) and nouns like 'Drogen' (drugs) or 'Waffen' (weapons).
Die Ermittler haben einen großen Schmuggler-Ring aufgedeckt.
The investigators uncovered a large smuggling ring.
group
'die Gruppe' and 'der Ring' can both refer to several people who work together. 'die Gruppe' is neutral and very general. It can occur at school, at work, or in free time. In this meaning, 'der Ring' means a group with a shared, often secret or illegal goal. That is why 'Ring' does not fit every normal group. Learners may confuse the words because both describe people as a unit. But 'Ring' sounds much more specific and often negative.

Die Polizei hat einen Ring von Betrügern entdeckt.
The police discovered a ring of fraudsters.
Für den Kurs bildet Herr Wolf eine Gruppe mit vier Teilnehmern.
For the course, Mr. Wolf forms a group with four participants.