Zero size group General forum

6 replies. Last post: 2020-06-14

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Zero size group
  • Sweaty Snooker Balls at 2020-06-13

    Does a group cease to exist if no members?

  • Carroll ★ at 2020-06-13

    Yes a group needs an identity element.

  • KPT ★ at 2020-06-13

    what are you talking about, exactly ?

  • isometry at 2020-06-13

    I second Carroll’s answer. Another possible interpretation is facebook groups. I don’t know if this is possible now, but a few years ago I had fun looking up obscure groups with no administrators, assigning myself the role of administrator, throwing out all members and then leave, so that the group disappeared.

  • Tom Ace at 2020-06-14

    I third Carroll’s answer. On a perhaps related topic, though, I remember some students in a high school math class having trouble with 0! being equal to 1.  By way of explanation, the teacher said “how many permutations are there of zero objects? one; there it is” and he pointed with his hands into empty space.

  • David J Bush ★ at 2020-06-14

    Actually a group doesn’t cease to exist if it didn’t exist in the first place.

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