Resting on a suitable base of the quotients of the lambda-series for the free groups on r generators, we get, for p odd, a class of TH-p-groups (n)G(r) with arbitrary large derived length. We prove that every TH-p-group G with r generators and exponent p(n) is a quotient of (n)G(r) and a product of m cyclic groups, where p(m) = Omega(1)(G)\. At last we describe the TH-p-groups of exponent p(2).
p-groups with all the elements of order p in the center / D. BUBBOLONI; CORSI TANI G. - In: ALGEBRA COLLOQUIUM. - ISSN 1005-3867. - STAMPA. - 11(2):(2004), pp. 181-190.
p-groups with all the elements of order p in the center
BUBBOLONI, DANIELA;
2004
Abstract
Resting on a suitable base of the quotients of the lambda-series for the free groups on r generators, we get, for p odd, a class of TH-p-groups (n)G(r) with arbitrary large derived length. We prove that every TH-p-group G with r generators and exponent p(n) is a quotient of (n)G(r) and a product of m cyclic groups, where p(m) = Omega(1)(G)\. At last we describe the TH-p-groups of exponent p(2).
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