Geodesic
On Some Sets of Group Functions
Matematičeskie zametki, Tome 74 (2003) no. 1, pp. 3-11.

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Let $G$ be a group, let $A$ be an Abelian group, and let $n$ be an integer such that $n\ge-1$. In the paper, the sets $\Phi_n(G,A)$ of functions from $G$ into $A$ of degree not greater than $n$ are studied. In essence, these sets were introduced by Logachev, Sal'nikov, and Yashchenko. We describe all cases in which any function from $G$ into $A$ is of bounded (or not necessarily bounded) finite degree. Moreover, it is shown that if $G$ is finite, then the study of the set $\Phi_n(G,A)$ is reduced to that of the set $\Phi_n(G/O^p(G),A_p)$ for primes $p$ dividing $|G/G'|$. Here $O^p(G)$ stands for the $p$-coradical of the group $G$, $A_p$ for the $p$-component of $A$, and $G'$ for the commutator subgroup of $G$. 
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M. I. Anokhin. On Some Sets of Group Functions. Matematičeskie zametki, Tome 74 (2003) no. 1, pp. 3-11. http://geodesic.mathdoc.fr/item/MZM_2003_74_1_a0/

[1] Logachëv O. A., Salnikov A. A., Yaschenko V. V., “Nekotorye kharakteristiki “nelineinosti” gruppovykh otobrazhenii”, Diskretnyi analiz i issledovanie operatsii (to appear)

[2] Likhtman A. I., “O gruppovykh koltsakh $p$-grupp”, Izv. AN SSSR. Ser. matem., 27:4 (1963), 795–800 | MR | Zbl

[3] Connell I. G., “On the group ring”, Canad. J. Math., 15:4 (1963), 650–685 | MR | Zbl

[4] Zimmermann K.-H., Beiträge zur algebraischen Codierungstheorie mittels modularer Darstellungstheorie, Bayreuther mathematische Schriften, 48, 1994

[5] Jennings S. A., “The structure of the group ring of a $p$-group over a modular field”, Trans. Amer. Math. Soc., 50:1 (1941), 175–185 | DOI | MR | Zbl

[6] Hill E. T., “The annihilator of radical powers in the modular group ring of a $p$-group”, Proc. Amer. Math. Soc., 25:4 (1970), 811–815 | DOI | MR | Zbl

[7] Berman S. D., “K teorii gruppovykh kodov”, Kibernetika, 1967, no. 1, 31–39 | Zbl