Equation 677 Database

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Magma e53aa0cfb20a…

magma e53aa0cfb20a
Size
595
Isomorphism class hash
e53aa0cfb20ab75c874c2a13032cb4c6029e2760034c51fe423250a882fad026
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
2026-10-06 12:39:04
Display reorder
169,170,166,167,165,168,100,99,101,97,98,96,125,124,123,122,120,121,479,478,474,475,476,477,507,506,508,509,504,505,530,537,526,584,592,174,176,175,178,179,177,54,56,55,57,58,59,157,156,155,158,161,159,152,154,153,149,150,151,191,187,195,183,256,253,232,234,233,235,236,237,246,245,244,247,248,249,107,106,105,103,104,102,319,318,320,321,322,323,293,292,288,289,290,291,466,465,467,462,463,464,414,419,415,416,417,418,470,469,471,472,473,468,498,503,499,500,501,502,378,383,379,380,381,382,324,329,325,326,327,328,536,527,519,534,551,549,539,543,559,586,568,561,583,585,569,576,228,227,226,229,230,231,240,239,238,243,241,242,250,254,180,193,185,189,90,92,91,93,94,95,132,134,133,136,137,135,35,34,33,32,30,31,129,131,130,127,128,126,204,203,202,206,207,205,453,452,454,455,450,451,402,407,403,404,405,406,356,355,357,358,359,354,424,423,425,420,421,422,332,331,333,334,335,330,281,280,276,277,278,279,305,304,300,301,302,303,370,369,371,366,367,368,540,552,550,525,531,513,548,532,589,580,570,558,572,574,578,566,6,8,7,10,11,9,144,143,145,147,148,146,160,142,141,138,139,140,47,46,45,44,42,43,4,3,5,2,1,0,71,70,69,68,66,67,75,77,76,73,74,72,49,48,50,51,52,53,316,315,317,312,313,314,442,441,443,438,439,440,449,448,444,445,446,447,349,348,350,351,352,353,491,490,486,487,488,489,347,346,342,343,344,345,306,311,307,308,309,310,398,397,399,400,401,396,535,515,533,514,522,521,511,510,594,591,557,571,588,554,565,555,209,208,210,213,211,212,198,197,196,201,199,200,252,257,181,194,186,190,64,63,65,61,62,60,29,28,27,24,25,26,83,82,81,80,78,79,87,89,88,85,86,84,172,171,173,162,163,164,461,460,456,457,458,459,340,339,341,336,337,338,430,429,431,426,427,428,387,386,388,389,384,385,410,409,411,412,413,408,266,265,267,268,269,264,262,261,263,259,258,260,274,273,275,270,271,272,541,538,544,520,524,523,545,512,593,581,563,562,567,573,560,556,110,109,108,111,112,113,15,17,16,12,13,14,117,119,118,115,116,114,39,41,40,36,37,38,188,184,192,182,255,251,222,221,220,225,223,224,216,215,214,217,218,219,18,20,19,23,21,22,361,360,362,363,364,365,481,480,482,483,484,485,497,496,492,493,494,495,434,433,435,436,437,432,298,297,299,294,295,296,376,375,377,372,373,374,284,283,285,286,287,282,394,393,395,390,391,392,529,516,518,517,546,547,528,542,553,582,575,590,577,579,564,587 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#21508ce76d8339c8cc8a9db508194b7933fb8eb19570d11d640cb6bc14178d14, M = the submagma generated by {0, 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 2026-10-06 12:39:05 · history