Grushko's theorem

The set of Grushko is a theorem from the mathematical field of group theory . It makes a statement about the rank of groups, i.e. their minimum number of producers .

Be and finally generated groups and their free product . Then applies ${\displaystyle A}$ ${\displaystyle B}$ ${\displaystyle A*B}$

${\displaystyle rk(A*B)=rk(A)+rk(B)}$.

The set was published in 1940 by Igor Alexandrovich Grushko and was part of his dissertation in Leningrad.

literature

• IA Grushko, On the bases of a free product of groups (Russian), Matematicheskii Sbornik, vol 8 (1940), pp. 169-182. On-line
• BH Neumann , On the number of generators of a free product, Journal of the London Mathematical Society, vol 18, (1943), pp. 12-20. On-line