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### Contents

Malcev A I On some classes of infinite soluble groups MajlbUeB | 28 |

Golovin O N On the isomorphism of nilpotent decompositions | 133 |

A Description of all irreducible unitary representations | 140 |

2 other sections not shown

### Common terms and phrases

3-dimensional space abelian group arbitrary automorphism central series centrally isomorphic refinements closed subset commutator subgroup commutator subgroup Aa complex components consider contains cosets cyclic groups decomposition of G deduce defined definition denote direct product direct sum direct summand eigenvalue eigenvectors element g endomorphisms of G equal factor group finite number formula free product group G groups Aa Hence holds homomorphism hypothesis idempotent infinitesimal rotations integral invariant subspaces irreducible representations Lemma Let G manifold mapping matrix g metabelian commutator subgroup metabelian product multiplication nilpotent group normal divisor obtain operator ordered with respect orthogonal partially ordered set Proof proved relation representation of weight rotation g rotation group satisfy the condition serving subgroup set of groups set of subgroups solvable group sphere spherical functions spinors of rank subgroup of G tensor of rank tensor representation Theorem tion transformation Tg unitary representation vector