# Senashov V. I.

### Characterizations of groups with almost layer-finite periodic part

↓ Abstract

Ukr. Mat. Zh. - 2017. - 69, № 7. - pp. 964-973

Construction of the set of finite subgroups of the form $L_g = \langle a, a^g\rangle$ in Shunkov’s groups is studying. As a corollary of this result follows two characterizations of groups with an almost layer-finite periodic part.

### On Sylow Subgroups of Some Shunkov Groups

↓ Abstract

Ukr. Mat. Zh. - 2015. - 67, № 3. - pp. 397-405

We study Shunkov groups with the following condition: the normalizer of any finite nontrivial subgroup has an almost layer-finite periodic part. Under this condition, we establish the structure of Sylow 2-subgroups in this group.

### On groups with a strongly imbedded subgroup having an almost layer-finite periodic part

Ukr. Mat. Zh. - 2012. - 64, № 3. - pp. 384-391

We study Shunkov groups with the following condition: the normalizer of any finite nonunit subgroup has an almost layer-finite periodic part. It is proved that such a group has an almost layer-finite periodic part if it has a strongly imbedded subgroup with almost layer-finite periodic part.

### Characterizations of the Shunkov groups

Ukr. Mat. Zh. - 2008. - 60, № 8. - pp. 1110–1118

The structure of the family of finite subgroups of the form *L _{g } * = ‹

*a, a*› in periodic Shunkov's group is studied. As a colorraries of the result obtained, two characterizations of periodic Shunkov's groups follow.

^{g }### On Frobenius groups with noninvariant factor *SL*_{ 2}(3)

Kozulin S. N., Senashov V. I., Shunkov V. P.

Ukr. Mat. Zh. - 2006. - 58, № 6. - pp. 765–777

We obtain a criterion for the unsimplicity of an infinite group containing the infinite class of the Frobenius groups $L_g = \langle a, g^{-1} a g\rangle$ with complement $SL_2 ( 3 )$.

### On Sylow subgroups of Shunkov periodic groups

Ukr. Mat. Zh. - 2005. - 57, № 11. - pp. 1548–1556

We study the structure of Sylow 2-subgroups in Shunkov periodic groups with almost layer-finite normalizers of finite nontrivial subgroups.

### Groups with handles of order different from three

Kozulin S. N., Senashov V. I., Shunkov V. P.

Ukr. Mat. Zh. - 2004. - 56, № 8. - pp. 1030–1042

We obtain a test for the unsimplicity of an infinite group.

### Characterization of Groups with a Layer-Finite Periodic Part

Ukr. Mat. Zh. - 2001. - 53, № 3. - pp. 383-391

We prove a theorem that characterizes groups with a layer-finite periodic part in the class of the Shunkov groups with solvable finite subgroups.

### Almost layer finiteness of a periodic group without involutions

Ukr. Mat. Zh. - 1999. - 51, № 11. - pp. 1529–1533

We prove a theorem that characterizes the class of almost layer finite groups in the class of periodic groups without involutions: If the normalizer of any nontrivial finite subgroup of a periodic conjugate biprimitive finite group without involutions is almost layer finite, then the group itself is almost layer finite.

### Sufficient conditions for the almost layer finiteness of groups

Ukr. Mat. Zh. - 1999. - 51, № 4. - pp. 472–485

We prove a theorem that describes almost layer-finite groups in the class of conjugatively biprimitive-finite groups.

### Groups satisfying the minimality condition for non-almost-layer-finite subgroups

Ukr. Mat. Zh. - 1991. - 43, № 7-8. - pp. 1002–1008