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12.1 (1992)

Partially Solved

H. Bass (Topology, 4, no. 4 (1966), 391–400) has constructed explicitly a proper subgroup of finite index in the group of units of the integer group ring of a finite cyclic group.
$\qquad$ a) Calculate the index of Bass’ subgroup.
$\qquad$ b) (A. A. Bovdi). Construct analogous subgroups for finite abelian non-cyclic groups.

Contributor: R. Zh. Aleev

Progress

b) They are constructed: for $p$-groups, $p \neq 2$, in (K. Hoechsmann, J. Ritter, J. Pure Apply. Algebra, 68, no. 3 (1990), 325–333); for the general case of groups of central units of integral group rings of arbitrary (not necessarily abelian) finite groups in (R. Zh. Aleev, Mat. Tr. Novosibirsk Inst. Math., 3, no. 1 (2000), 3–37 (Russian)).

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