Equation 677 Database

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Magma 99852255889b…

magma 99852255889b
Size
595
Isomorphism class hash
99852255889b87702ffe0da0dd8991334359bd9ba8882c967e6634e18580cabe
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 22:58:43
Display reorder
501,500,502,503,499,498,495,494,496,497,493,492,298,297,299,294,295,296,506,505,507,508,509,504,272,270,271,274,275,273,515,591,592,593,594,370,366,371,368,369,367,336,341,337,338,339,340,347,346,342,343,344,345,348,353,349,350,351,352,354,359,355,356,357,358,372,377,373,374,375,376,360,365,361,362,363,364,17,16,15,13,14,12,231,233,232,228,229,230,21,23,22,20,18,19,117,119,118,116,115,114,189,191,190,187,188,186,244,243,245,240,242,241,28,27,29,24,25,26,123,125,124,120,122,121,159,161,160,158,156,157,545,525,530,519,555,535,514,550,540,565,585,580,560,570,574,590,316,312,317,314,315,313,458,457,459,460,461,456,463,462,464,465,466,467,482,481,483,484,485,480,470,469,471,472,473,468,323,322,318,319,320,321,476,475,477,478,479,474,104,106,105,103,101,102,225,227,226,222,223,224,91,90,89,93,94,92,5,4,3,0,2,1,208,207,209,206,204,205,263,265,264,266,267,268,95,97,96,100,98,99,147,149,148,145,146,144,177,179,178,176,174,175,542,524,529,516,554,534,513,549,539,564,584,579,556,569,573,589,310,306,311,308,309,307,446,445,447,448,449,444,451,450,452,453,454,455,436,435,437,432,433,434,442,441,443,438,439,440,300,305,301,302,303,304,430,429,431,426,427,428,75,74,76,71,72,73,219,221,220,216,217,218,79,78,77,81,82,80,6,7,8,9,10,11,202,201,203,200,198,199,257,259,258,260,261,262,83,85,84,88,86,87,141,143,142,139,140,138,171,173,172,170,168,169,543,523,528,517,553,533,512,548,538,563,583,578,559,568,575,588,277,278,276,280,281,279,397,396,398,399,400,401,402,407,403,404,405,406,414,419,415,416,417,418,420,425,421,422,423,424,395,394,390,391,392,393,408,413,409,410,411,412,67,66,113,68,69,70,210,211,212,214,215,213,55,54,56,57,58,59,53,52,51,49,50,48,193,192,194,197,195,196,255,254,256,252,253,251,62,61,60,64,65,63,133,132,134,137,135,136,163,162,164,165,166,167,541,521,527,520,552,532,510,547,537,562,581,576,557,566,571,586,379,381,380,383,378,382,328,327,329,324,325,326,333,332,334,335,330,331,291,290,292,293,288,289,489,488,490,491,486,487,387,386,388,389,384,385,285,284,286,287,282,283,109,108,107,111,112,110,234,236,235,237,238,239,38,37,36,40,41,39,33,35,34,32,30,31,183,185,184,180,182,181,249,269,250,246,247,248,43,42,44,45,46,47,126,128,127,130,131,129,154,153,155,151,150,152,544,522,526,518,551,531,511,546,536,561,582,577,558,567,572,587 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#a68686773c1c84a50fc680c2f9bbdb3f90f3c80b3d983f347231cff070658488, M = the submagma generated by {18, 24} (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 22:58:44 · history