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- W2488249068 abstract "Base (minimal generating set) of the Sylow 2-subgroup of (S_{2^n}) is called diagonal if every element of this set acts non-trivially only on one coordinate, and different elements act on different coordinates. The Sylow 2-subgroup (P_n(2)) of (S_{2^n}) acts by conjugation on the set of all bases. In presented paper the~stabilizer of the set of all diagonal bases in (S_n(2)) is characterized and the orbits of the action are determined. It is shown that every orbit contains exactly (2^{n-1}) diagonal bases and (2^{2^n-2n}) bases at all. Recursive construction of Cayley graphs of (P_n(2)) on diagonal bases ((ngeq2)) is proposed." @default.
- W2488249068 created "2016-08-23" @default.
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- W2488249068 date "2016-07-12" @default.
- W2488249068 modified "2023-09-26" @default.
- W2488249068 title "The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs" @default.
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