On large cyclic subgroups of finite groups

Author:
Edward A. Bertram

Journal:
Proc. Amer. Math. Soc. **56** (1976), 63-66

MathSciNet review:
0399019

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Abstract: It is known that for each (composite) every group of order contains a proper subgroup of order greater than . We prove that given , for almost all , as , every group of order contains a characteristic cyclic subgroup of square-free order , and provide an upper bound to the number of exceptional . This leads immediately to a like density result for a lower bound to the number of conjugacy classes in .

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DOI:
https://doi.org/10.1090/S0002-9939-1976-0399019-5

Article copyright:
© Copyright 1976
American Mathematical Society