The next value, gnu(2048), is still not precisely known, but it strictly exceeds 1774274116992170, which is the exact number of groups of order 2048 that have exponent-2 class 2, and can confidently be expected to agree with that number in its first 3 digits.
I'm forced to feel that someone, somewhere, is trolling...
The next value, gnu(2048), is still not precisely known, but it strictly exceeds 1774274116992170, which is the exact number of groups of order 2048 that have exponent-2 class 2, and can confidently be expected to agree with that number in its first 3 digits.
I'm forced to feel that someone, somewhere, is trolling...
I didn't know what I was doing - I was just taking a punt. I've never studied groups.
I'm forced to feel that someone, somewhere, is trolling...
If OP simply missed out the condition "abelian", then it becomes a reasonable question (being the result of an exercise in the use of the Structure Theorem).
If OP simply missed out the condition "abelian", then it becomes a reasonable question (being the result of an exercise in the use of the Structure Theorem).
Possible, but:
1) That's a pretty sloppy error to make at this level. 2) It's a bit of a coincidence that 2048 is the smallest number for which the answer is unknown.
1) That's a pretty sloppy error to make at this level. 2) It's a bit of a coincidence that 2048 is the smallest number for which the answer is unknown.
i am doing a course at the moment in probabilistic group theory, and I realized one of the questions in the book would be very simple if I knew the number of groups (up to isomorphism obviously) of order 2048 - evidently the author realized that too when asking the question!