Torsion elements in p-adic analytic pro-p groups

✍ Scribed by Lawrence E. Wilson

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 263 KB
• Volume: 277
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(03)00534-9

✦ Synopsis

A finitely generated pro-p group is p-adic analytic if and only if there exists m and h with m < p h such that the mth term of the lower central series of the group is contained in the subgroup generated by the p h th powers of elements of the group. Recent work has shown that if m 2p -3 then the torsion elements form a subgroup. An example shows that if m h(p -1) + 1 with h 2 then the torsion elements need not form a subgroup. We prove for odd primes p that if m h(p -1) then the torsion elements do form a subgroup and provide an explicit bound on the order of the product of two elements of order dividing p i in terms of i, h, and p.