Geodesic
Conjugacy growth in the higher Heisenberg groups
Glasgow mathematical journal, Tome 65 (2023), pp. S148-S169

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DOI

We calculate asymptotic estimates for the conjugacy growth function of finitely generated class 2 nilpotent groups whose derived subgroups are infinite cyclic, including the so-called higher Heisenberg groups. We prove that these asymptotics are stable when passing to commensurable groups, by understanding their twisted conjugacy growth. We also use these estimates to prove that, in certain cases, the conjugacy growth series cannot be a holonomic function.
DOI : 10.1017/S0017089522000428
Mots-clés : conjugacy growth, nilpotent groups, Heisenberg groups, twisted conjugacy 
Evetts, Alex. Conjugacy growth in the higher Heisenberg groups. Glasgow mathematical journal, Tome 65 (2023), pp. S148-S169. doi: 10.1017/S0017089522000428
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     author = {Evetts, Alex},
     title = {Conjugacy growth in the higher {Heisenberg} groups},
     journal = {Glasgow mathematical journal},
     pages = {S148--S169},
     year = {2023},
     volume = {65},
     number = {S1},
     doi = {10.1017/S0017089522000428},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089522000428/}
}
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