On periodic groups with an almost regular involution

Some groups of exponent 72

“…Lemma 2.1 (V. P. Shunkov [13]). If a periodic group G contains an involution t with finite centralizer C G .t /, then G is locally finite.…”

Arrangement of elements of prime orders in groups

“…This proposition is actually proved in [9], where the condition of periodicity of the whole group is not an essential restriction, under the condition of finiteness of the sugroups gr (~',i ~) , ~…”

On Local Finiteness of Periodic Residually Finite Groups

“…In fact, Shalev's results show that in the case in which A is a finite 2-group, the hypothesis that A, A g is finite for any g ∈ G can be omitted (if A is of order 2, then, by virtue of Shunkov's theorem [10], even the assumption that G is residually finite is not required). It seems, however, that the 2-group case is special and in general the hypothesis on A, A g , or something similar, is necessary.…”