Equation 677 Database

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Magma a6b75fdf619b…

magma a6b75fdf619b
Size
595
Isomorphism class hash
a6b75fdf619be4878982794ef0b7d3424292095bdacf9c0c0a9d3feae1fa5e16
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 12:41:37
Display reorder
160,159,161,158,156,157,168,170,169,172,173,171,133,132,134,137,135,136,423,422,424,425,420,421,385,384,386,387,388,389,538,536,532,585,565,131,129,128,126,127,130,84,83,85,81,82,80,164,163,162,167,165,166,178,177,179,175,176,174,195,191,187,183,256,253,226,225,227,229,228,249,217,216,218,214,215,236,31,30,32,27,28,29,464,463,465,466,467,462,416,415,417,418,419,414,269,268,264,265,266,267,391,390,392,393,394,395,336,341,337,338,339,340,263,262,259,258,260,261,460,459,461,456,457,458,335,334,330,331,332,333,512,550,518,531,539,548,543,537,584,581,590,593,573,580,555,572,202,203,205,206,207,204,239,238,237,242,240,241,250,254,180,189,193,185,13,12,14,10,11,9,74,76,75,77,78,79,16,15,17,20,18,19,50,49,48,47,45,46,208,210,209,213,211,212,468,473,469,470,471,472,486,491,487,488,489,490,398,397,399,400,401,396,504,509,505,506,507,508,451,450,452,453,454,455,278,277,279,280,281,276,270,275,271,272,273,274,301,300,302,303,304,305,546,515,551,545,524,510,517,540,586,582,591,568,571,567,576,588,102,103,105,106,104,101,153,155,154,150,151,152,64,63,62,67,65,66,118,117,116,115,113,114,68,70,69,71,72,73,91,90,89,86,87,88,60,125,61,57,58,59,5,4,3,7,8,6,284,283,285,286,287,282,482,481,483,484,485,480,502,501,503,498,499,500,445,444,446,447,448,449,479,478,474,475,476,477,362,361,363,364,365,360,356,355,357,358,359,354,317,316,312,313,314,315,513,530,535,521,526,519,529,527,594,554,575,569,557,564,570,566,220,221,223,224,222,219,197,196,198,200,201,199,252,257,181,190,194,186,51,53,52,54,55,56,22,21,23,25,26,24,122,124,123,120,121,119,41,40,39,44,42,43,138,140,139,143,141,142,374,373,375,376,377,372,432,437,433,434,435,436,411,410,412,413,408,409,494,493,495,496,497,492,429,428,430,431,426,427,371,370,366,367,368,369,378,383,379,380,381,382,348,353,349,350,351,352,533,516,544,547,522,528,511,541,592,559,583,579,558,577,589,574,144,145,147,148,149,146,35,34,33,38,36,37,110,112,111,107,108,109,98,100,99,2,1,0,192,188,184,182,255,251,233,235,234,231,232,230,248,247,246,245,243,244,96,95,97,92,93,94,318,323,319,320,321,322,406,405,407,402,403,404,442,441,443,438,439,440,297,296,298,299,294,295,343,342,344,345,346,347,308,307,309,310,311,306,291,290,292,293,288,289,329,328,324,325,326,327,520,552,514,534,525,549,542,523,553,556,563,587,560,561,562,578 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 {6, 18} (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 12:41:39 · history