The structure of maximal tori in spin groups of type $D_l$
We determine the abelian invariants of the maximal tori in the finite spin groups of type $D_l$
math.GR↗
arXiv subjects
Andrei V. Zavarnitsine
Publications and source records attributed to Andrei V. Zavarnitsine.
On a finite 2,3-generated group of period 12
Using calculations in computer algebra systems along with some theoretic results, we construct the largest finite group of period 12 generated by an element of order 2 and an element of order 3. In particular, we prove that this group has order $2^{66}.3^7$.
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Abelian-by-cyclic Moufang loops
We use groups with triality to construct a series of nonassociative Moufang loops. Certain members of this series contain an abelian normal subloop with the corresponding quotient being a cyclic group. In particular, we give a new series of examples of finite abelian-by-cyclic Moufang loops. The previously known [A. Rajah, J. Alg., 235 (2001), 66-93] loops of this type of odd order 3q^3, with prime q congruent to 1 mod 3, are particular cases of our series. Some of the examples are shown to be embeddable into a Cayley algebra.
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A solvable group isospectral to S(4,3)
We construct a solvable group G of order 5648590729620 such that the set of element orders of G coincides with that of the simple group S(4,3). This completes the determination of finite simple groups isospectral to solvable groups.
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Finite simple groups with narrow prime spectrum
We find the nonabelian finite simple groups with order prime divisors not exceeding 1000. More generally, we determine the sets of nonabelian finite simple groups whose maximal order prime divisor is a fixed prime less than 1000. Our results are based on calculations in the computer algebra system GAP.
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Properties of element orders in covers for L(n,q) and U(n,q)
We show that if a finite simple group G isomorphic to PSL(n,q) or PSU(n,q), where either $n\ne 4$, or q is prime or even, acts on a vector space over a field of the defining characteristic of G, then the corresponding semidirect product contains an element whose order is distinct from every element order of G. As a consequence, we prove that the group PSL(n,q), where $n\ne 4$ or q prime or even, is recognizable by spectrum from its covers thus giving a partial positive answer to Problem 14.60 from the Kourovka notebook.
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Sylow's theorem for Moufang loops
For finite Moufang loops, we prove an analog of the first Sylow theorem giving a criterion of the existence of a p-Sylow subloop. We also find the maximal order of p-subloops in the Moufang loops that do not possess p-Sylow subloops.
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