1992
DOI: 10.1093/qmath/43.2.157
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METABELIAN THIN p-GROUPS

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Cited by 15 publications
(26 citation statements)
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“…Another class of Lie algebras that has been widely studied is that of thin Lie algebras [2,12]. A graded Lie algebra L = i≥1 L i is said to be thin when dim(L i ) ≤ 2 for all i, and the following covering property holds: for all i, and for every 0 = v ∈ L i , one has [vL 1 ] = L i+1 .…”
Section: Introductionmentioning
confidence: 99%
“…Another class of Lie algebras that has been widely studied is that of thin Lie algebras [2,12]. A graded Lie algebra L = i≥1 L i is said to be thin when dim(L i ) ≤ 2 for all i, and the following covering property holds: for all i, and for every 0 = v ∈ L i , one has [vL 1 ] = L i+1 .…”
Section: Introductionmentioning
confidence: 99%
“…It is also well known that M M has a presentation with integer structure constants. Also, by w x Corollary 1.6 of 6 , a finitely generated just-infinite graded Lie algebra of finite coclass generated by L over a field of characteristic 0 is isomorphic 1 to M M. Combining these two results we get that there exists a unique infinite-dimensional soluble graded Lie algebra of finite coclass generated by L with structure constants in ‫,ޚ‬ namely the Lie algebra M M. 1 …”
Section: P3 For Every Homogeneous Ideal I There Exists a Natural Numbermentioning
confidence: 79%
“…Now R < M*' D A/2 2 for some x x , x 2 e G and by the above, we have /? < M, n M 2 = ), and [T:R]=p 2 implies fl = $(7). Hence fl<G, as claimed.…”
Section: Rolf Brandl and Libero Verardi Corresponds To Y Via The Assumentioning
confidence: 99%
“…Clearly, ^(G) contains the lattice -A"(G) of all normal subgroups of G, and we conjecture that cp(Jf(G)) = Jf (H), that is <p maps normal subgroups of G onto normal subgroups of H. Indeed Proposition 3.4 below and the subsequent remark provide an affirmative answer in a special case. The conjecture would easily imply that, if G is of maximal class or thin (see [2]), then H has the analogous property. We do not have a counterexample to this, but the following shows that G and H may be of different nilpotency class and <p ([Z(G)…”
Section: Let G and H Be Metacyclic P-groups And Assume That Cp: 'S(g)mentioning
confidence: 99%