Geodesic
Infinite groups of finite period
Algebra i logika, Tome 54 (2015) no. 2, pp. 243-251

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It is proved that there exist periodic groups containing an element of even order and only trivial normal $2$-subgroups in which every pair of involutions generates a $2$-group. This gives a negative answer to Question 11.11a in the Kourovka Notebook. Furthermore, we point out examples of finite simple groups that are recognizable by spectrum in the class of finite groups but not recognizable in the class of all groups.
Keywords: periodic group, periodic product, spectrum of group, recognizability by spectrum, Baire–Suzuki theorem, modular group. 
@article{AL_2015_54_2_a6,
     author = {V. D. Mazurov and A. Yu. Ol'shanskii and A. I. Sozutov},
     title = {Infinite groups of finite period},
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     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2015_54_2_a6/}
}
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V. D. Mazurov; A. Yu. Ol'shanskii; A. I. Sozutov. Infinite groups of finite period. Algebra i logika, Tome 54 (2015) no. 2, pp. 243-251. http://geodesic.mathdoc.fr/item/AL_2015_54_2_a6/