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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 …
Stefan Kohl's user avatar
  • 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 …
Stefan Kohl's user avatar
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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 …
Stefan Kohl's user avatar
  • 19.6k