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Results tagged with open-problems
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user 28104
If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"
5
votes
Bounds on number of conjugacy classes in terms of number of elements of a group ?
In the meantime, Barbara Baumeister, Attila Maróti and Hung P. Tong-Viet
have obtained a better lower bound on the number of conjugacy classes of
a group of given order. -- Namely, in 2015 they have p …
- 19.6k
37
votes
PhD dissertations that solve an established open problem
The thesis of Martin Hertweck answered the at that time 60-years-old
isomorphism problem for integral group rings in the negative, by constructing
a counterexample. That is, a pair of non-isomorphic f …
10
votes
Accepted
Is it true that every f.g. infinite simple group has exponential growth?
No, there exists a finitely generated infinite simple group of intermediate
growth. This has meanwhile been found out by Volodymyr Nekrashevych, cf.
Palindromic subshifts and simple periodic groups o …
- 19.6k
16
votes
1
answer
913
views
Is it true that every f.g. infinite simple group has exponential growth?
Is it true that every finitely generated infinite simple group has
exponential (word-)growth?
Remark: As Mark Sapir has pointed out, the question whether
every finitely generated group of subexponent …
- 19.6k