2019
Том 71
№ 6

All Issues

Senashov V. I.

Articles: 11
Article (Russian)

Characterizations of groups with almost layer-finite periodic part

Senashov V. I.

↓ 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.

Article (Russian)

On Sylow Subgroups of Some Shunkov Groups

Senashov V. I.

↓ 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.

Article (Russian)

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

Senashov V. I.

↓ Abstract   |   Full text (.pdf)

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.

Article (Russian)

Characterizations of the Shunkov groups

Senashov V. I.

↓ Abstract   |   Full text (.pdf)

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

The structure of the family of finite subgroups of the form Lg = ‹a, ag › in periodic Shunkov's group is studied. As a colorraries of the result obtained, two characterizations of periodic Shunkov's groups follow.

Article (Russian)

On Frobenius groups with noninvariant factor SL 2(3)

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

↓ Abstract   |   Full text (.pdf)

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 $SL_2 ( 3 )$.

Article (Russian)

On Sylow subgroups of Shunkov periodic groups

Senashov V. I.

↓ Abstract   |   Full text (.pdf)

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.

Article (Russian)

Groups with handles of order different from three

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

↓ Abstract   |   Full text (.pdf)

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

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

Article (Russian)

Characterization of Groups with a Layer-Finite Periodic Part

Senashov V. I.

↓ Abstract   |   Full text (.pdf)

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.

Article (Russian)

Almost layer finiteness of a periodic group without involutions

Senashov V. I.

↓ Abstract   |   Full text (.pdf)

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.

Article (Russian)

Sufficient conditions for the almost layer finiteness of groups

Senashov V. I.

↓ Abstract   |   Full text (.pdf)

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.

Article (Ukrainian)

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

Senashov V. I.

Full text (.pdf)

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