Conditions, under which projective Sylow subgroups of almost locally normal group are locally conjugate

O.M. Tkachenko (Prydniprovsk State Academy of Building and Architecture)


Two subclasses of expansions of locally normal groups with the help of finite p-groups are selected, at which projective Sylow p-subgroups are locally conjugate. The subgroup F of a finite index contains in the first case invariant Sylow p-subgroup, in the second case Sylow p-subgroups in F are almost abelian. The example that is given shows that for both subclasses the condition of expansion of locally normal group with the help of just p-group is essential.


Tkachenko O.M. "Sylow subgroups of almost locally normal groups", Ukrainian Math. J., 1984; 36(6): pp. 798-801. (in Russian) doi:10.1007/BF01268440

Tkachenko O.M. "Conditions of local conjugation of Sylow subgroups in almost locally normal group", Matem. studii, 2008; 29(2): pp. 127-131. (in Ukrainian)

Tkachenko O.M. "Almost locally normal groups, all Sylow subgroups of which are projective", Nauk. visnyk NGU, 2005; 8: pp. 74-76. (in Ukrainian)

Tkachenko O.M. "Condition of isomorphism of Sylow subgroups of almost locally normal group", Res. Math., 2005; 13: pp. 102-103. (in Ukrainian)




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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991