Geodesic
A reduction theorem for perfect locally finite minimal non-FC groups
Glasgow mathematical journal, Tome 41 (1999) no. 1, pp. 81-83

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A group G is said to be a minimal non-FC group, if G contains an infinite conjugacy class, while every proper subgroup of G merely has finite conjugacy classes. The structure of imperfect minimal non-FC groups is quite well-understood. These groups are in particular locally finite. At the other end of the spectrum, a perfect locally finite minimal non-FC group must be a p-group. And it has been an open question for quite a while now, whether such groups exist or not. 
LEINEN, FELIX. A reduction theorem for perfect locally finite minimal non-FC groups. Glasgow mathematical journal, Tome 41 (1999) no. 1, pp. 81-83. doi: 10.1017/S001708959997043X
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