Burichenko, V. P.
Published in
Mathematical Notes

It is proved that every finite group G can be represented as the quotient group of some finite group K such that all elements of “small” primary orders in K generate an Abelian normal subgroup.

Bendikov, Alexander Pittet, Christophe Sauer, Roman

We give a formula relating the $L^2$-isoperimetric profile to the spectral distribution of the Laplace operator associated to a finitely generated group $\Gamma$ or a Riemannian manifold with a cocompact, isometric $\Gamma$-action. As a consequence, we can apply techniques from geometric group theory to estimate the spectral distribution of the Lap...

Ebanks, Bruce
Published in
Aequationes mathematicae

The general solution of the functional equation f(xy) = f(x)h(y) + f(y) on abelian groups is well-known. We present methods for solving this equation on various non-abelian groups. In particular we treat the equation on semidirect products, then extend this treatment to solvable groups. We also find the solution on perfect groups. These results als...

Lutsenko, Yu. V. Skiba, A. N.
Published in
Mathematical Notes

In the paper, the precise structure of finite groups all of whose second (or all of whose third) maximal subgroups are subnormal is established.

Al-Sharo, Kh. A.
Published in
Mathematical Notes

Let Gbe a finite group. A subgroup H of G is said to be S-permutable in G if HP = PH for all Sylow subgroups P of G. A subgroup A of a group G is said to be S-permutably embedded in G if for each Sylow subgroup of A is also a Sylow of some S-permutable subgroup of G. In this paper, we analyze the following generalization of this concept. Let H be a...

Babai, László Qiao, Youming

We consider the problem of testing isomorphism of groups of order n given by Cayley tables. The trivial n^{log n} bound on the time complexity for the general case has not been improved over the past four decades. Recently, Babai et al. (following Babai et al. in SODA 2011) presented a polynomial-time algorithm for groups without abelian normal sub...

Kamornikov, S. F.
Published in
Mathematical Notes

In the paper, continuummany natural transitive lattice subgroup functors corresponding to no hereditary lattice formation are constructed on the class of all finite groups. This result is an answer to Question 15.39 in “The Kourovka Notebook”, which was posed by the author and A. F. Vasil’ev in connection with their theorem claiming that, on the cl...

Knyagina, V. N. Monakhov, V. S.
Published in
Proceedings of the Steklov Institute of Mathematics

A Schmidt group is a finite nonnilpotent group in which every proper subgroup is nilpotent. Sufficient conditions are established for the p-solvability of a finite group in which a Sylow p-subgroup is permutable with some Schmidt subgroups. Sufficient conditions for the solvability of a finite group in which some Schmidt subgroups are permutable ar...

Otera, Daniele Ettore Russo, Francesco
Published in
Mediterranean Journal of Mathematics

The property of quasi-simple filtration (or qsf) for groups has been introduced in literature more than 10 years ago by S. Brick. This is equivalent, for groups, to the weak geometric simple connectivity (or wgsc). The main interest of these notions is that there is still not known whether all finitely presented groups are wgsc (qsf) or not. The pr...

Kong, Q.
Published in
Mathematical Notes