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In mathematical finite group theory, the B-theorem (formerly the B-conjecture) states that if C is the centralizer of an involution of a finite group, then every component of C/O(C) is the image of a component of C (Gorenstein 1983, p. 7 and chapter 3).
References

Gorenstein, D. (1983), The classification of finite simple groups. Vol. 1, The University Series in Mathematics, Plenum Press, ISBN 978-0-306-41305-6, MR 746470

Mathematics Encyclopedia