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C-group

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For the culture in ancient Nubia, see C-Group.

In mathematical group theory, a C-group is a group such that the centralizer of any involution has a normal Sylow 2-subgroup.

The simple C-groups were determined by Suzuki (1965), and his classification is summarized by Gorenstein (1980, 16.4). The classification of C-groups was used in Thompson's classification of N-groups.

References

  • Gorenstein, D. (1980), Finite Groups, New York: Chelsea, ISBN 978-0-8284-0301-6, MR81b:20002
  • Suzuki, Michio (1965), "Finite groups in which the centralizer of any element of order 2 is 2-closed", Annals of Mathematics. Second Series, 82: 191–212, ISSN 0003-486X, MR0183773
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