Equation 677 Database

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Magma 9947e77af599…

magma 9947e77af599
Size
595
Isomorphism class hash
9947e77af5999bbecdcc87ba51416fa5bbe772808ec1d231485ed2f892599865
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 20:23:17
Display reorder
65,64,63,60,61,62,337,336,338,339,340,341,332,331,333,334,335,330,505,504,506,507,508,509,502,501,503,499,498,500,515,593,594,561,562,2,1,5,3,4,0,269,268,267,264,265,266,228,229,230,232,233,231,174,176,175,178,179,177,281,280,279,278,277,276,166,165,167,163,164,162,238,237,239,234,236,235,169,168,170,173,171,172,8,7,6,11,9,10,160,159,161,156,157,158,423,422,424,425,420,421,413,412,408,409,410,411,417,416,418,419,414,415,404,403,405,406,407,402,487,486,488,489,490,491,453,452,454,455,451,450,545,525,535,547,510,530,532,531,551,558,580,564,589,569,574,581,151,152,154,155,153,150,263,262,261,258,259,260,140,139,138,143,141,142,126,128,127,130,131,129,299,298,297,296,294,295,118,117,119,115,116,114,135,137,136,132,133,134,121,120,122,125,123,124,240,241,242,244,245,243,149,148,147,145,146,144,387,386,388,389,384,385,377,376,372,373,374,375,381,380,382,383,378,379,390,395,391,392,393,394,485,484,480,481,482,483,400,399,401,396,397,398,544,523,534,548,524,521,533,522,554,557,578,563,591,571,576,579,198,199,201,202,203,200,273,275,274,271,272,270,225,227,226,222,223,224,204,206,205,208,209,207,304,303,305,301,302,300,189,191,190,186,187,188,213,215,214,210,211,212,182,181,180,183,184,185,192,194,193,195,196,197,219,221,220,218,216,217,459,458,460,461,457,456,427,426,428,429,430,431,443,442,438,439,440,441,449,448,444,445,446,447,496,495,497,492,493,494,434,433,435,436,437,432,549,529,527,546,536,537,526,528,552,560,582,565,588,570,573,583,22,23,19,20,18,21,249,251,250,246,248,247,25,24,26,28,29,27,51,53,52,49,50,48,284,283,282,287,285,286,40,39,41,37,38,36,54,56,55,57,58,59,43,42,44,47,45,46,16,15,17,13,14,12,34,33,35,30,31,32,463,467,462,464,465,466,323,322,318,319,320,321,329,328,324,325,326,327,316,315,317,312,313,314,471,470,472,473,469,468,306,307,308,309,310,311,550,512,511,541,539,540,513,514,555,559,586,567,592,568,577,587,113,111,110,108,109,112,253,252,254,257,255,256,94,93,95,91,92,90,83,82,81,78,79,80,288,290,289,291,292,293,66,68,67,69,70,71,86,85,84,89,87,88,75,77,76,73,74,72,107,106,105,104,102,103,97,96,98,99,100,101,358,357,359,354,355,356,342,347,343,344,345,346,352,351,353,348,349,350,361,360,362,363,364,365,474,479,475,476,477,478,369,368,370,371,366,367,542,518,519,543,520,538,516,517,553,556,584,566,590,572,575,585 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#21508ce76d8339c8cc8a9db508194b7933fb8eb19570d11d640cb6bc14178d14, M = the submagma generated by {36, 78} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 85.

last edited by qawbecrdtey at 2026-10-08 20:23:18 · history