S. N. Kozulin, V. I. Senashov, V. P. Shunkov, “<nobr>$M_p$</nobr>-groups not containing groups of quaternions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, Number 2,Pages <nobr>17

$M_p$-groups not containing groups of quaternions

S. N. Kozulin^a, V. I. Senashov^bc, V. P. Shunkov^b

^a "VTB24 Lizing" joint stock company, 20 Daev Lane, Moscow, 107045 Russia
^b Institute of Computational Modelling, Siberian Branch of Russian Academy of Sciences, 50/44 Akademgorodok, Krasnoyarsk, 660036 Russia
^c Chair of Algebra and Mathematical Logic, Siberian Federal University, 79 Svobodnyi Ave., Krasnoyarsk, 660041 Russia

Abstract: This paper continues the study of class of $M_p$-groups introduced by V. P. Shunkov. We obtain a criterion of non-simplicity of an infinite group, which contains the $M_p$-group and contains no group of quaternions. We also obtain a criterion that an infinite group is the $M_p $-group.

Keywords: group, finiteness condition, Frobenius group.

UDC: 512.54

Received: 26.01.2012
Revised: 21.01.2013