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Apr 9, 2018 at 16:12 comment added Thomas This problem has been studied in a more general (and sligthly different) context by Ekatarina Pervova and Carlo Petronio in a nice paper Complexity and T ‐invariant of Abelian and Milnor groups, and complexity of 3‐manifoldshttps://onlinelibrary.wiley.com/doi/pdf/10.1002/mana.200510669
Apr 9, 2018 at 8:16 history edited Derek Holt CC BY-SA 3.0
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Apr 9, 2018 at 8:11 comment added YCor To get lower bounds you might already look for lower bounds in the variety of abelian groups of exponent dividing $173^2$.
Apr 9, 2018 at 8:09 history edited Derek Holt CC BY-SA 3.0
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Apr 9, 2018 at 7:53 history answered Derek Holt CC BY-SA 3.0