Geodesic
The Augmentation Terminals of Certain Locally Finite Groups
Canadian journal of mathematics, Tome 24 (1972) no. 2, pp. 221-238

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Let G be a group and ZG be the integral group ring of G. We shall write g for the augmentation ideal of G; that is to say, the kernel of the homomorphism of ZG onto Z which sends each group element to 1. The powers gλ of g are defined inductively for ordinals λ by gλ = gμg, if λ = μ + 1, and otherwise. The first ordinal λ for which gλ = gλ+1 is called the augmentation terminal or simply the terminal of G. For example, if G is either a cyclic group of prime order or else isomorphic with the additive group of rational numbers then gn > gω = 0 for all finite n, so that these groups have terminal ω.The groups with finite terminal are well-known and easily described. If G is one such, then every homomorphic image of G must also have finite terminal. 
Gruenberg, K. W.; Roseblade, J. E. The Augmentation Terminals of Certain Locally Finite Groups. Canadian journal of mathematics, Tome 24 (1972) no. 2, pp. 221-238. doi: 10.4153/CJM-1972-018-5
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[1] 1. Baer, R., Irreducible groups of automorphisms of abelian groups, Pacific J. Math. 14 (1964), 385–406. Google Scholar

[2] 2. Gruenberg, K. W., The residual nilpotence of certain presentations of finite groups, Arch. Math. 18 (1962), 408–417. Google Scholar

[3] 3. Gruenberg, K. W., Cohomological topics in group theory, Lecture Notes in Mathematics, No. 143 (Springer, New York, 1970). Google Scholar

[4] 4. Hartley, B., The residual nilpotence of wreath products, Proc. London Math. Soc. 20 (1970), 365–392. Google Scholar

[5] 5. Mal'cev, A. I., Generalized nilpotent algebras and their adjoint groups, Mat. Sbornik N.S. 25 (67), (1949), 347–366, (Russian), and Amer. Math. Soc. Translations (2), 69, (1968), 1-21. Google Scholar

[6] 6. Robinson, D. J. S., A property of the lower central series of a group, Math. Z. 107 (1968), 225–231. Google Scholar

[7] 7. Roseblade, J. E., The permutability of orthogonal subnormal subgroups, Math. Z. 90 (1965), 365–372. Google Scholar

[8] 8. Schenkman, E., The splitting of certain solvable groups, Proc. Amer. Math. Soc. 6 (1955), 286–290. Google Scholar

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