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- W2000332101 abstract "each a subgroup of prime index in the preceding. He outlines a proof2 that each group with k 1) of 22 .313 is Il(mod 7); and the normalizer5 in G of each Sylow subgroup of order 7 is of order 2.7. A subgroup, H, of index 3 or 13 in G could have only one Sylow subgroup of order 7, necessarily normal in H of order respectively 22 7 *13 or 22.3 7, both of which are larger than 2*7. Hence, G has no subgroup of index 3 or 13. G has 2-7 Sylow subgroups of order 13; the normalizer in G of each is of order 2-3-13. A subgroup, M, of index 7 in G could have only one Sylow subgroup of order 13, normal in M of order 22 .3*13 >2 3 13. And G has no subgroup of index 7. In the direct product of G above and any solvable group, each subgroup of prime index must contain G. Hence, for each integer n ?5, there exists a group with n factors in its order not satisfying the condition. UNIVERSITY OF TEXAS" @default.
- W2000332101 created "2016-06-24" @default.
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- W2000332101 date "1951-06-01" @default.
- W2000332101 modified "2023-09-26" @default.
- W2000332101 title "On a question raised by Garrett Birkhoff" @default.
- W2000332101 doi "https://doi.org/10.1090/s0002-9939-1951-0045112-9" @default.
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