Equation 677 Database

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Magma c2645a7acd04…

magma c2645a7acd04
Size
595
Isomorphism class hash
c2645a7acd0415960a61cac35c004bca380697537bd9d0235a6bc52e790662ed
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
2026-10-07 07:36:26
Display reorder
506,507,508,509,505,504,437,436,432,433,434,435,441,440,442,443,438,439,445,444,446,447,448,449,272,270,271,274,275,273,555,592,591,593,594,498,503,499,500,501,502,386,385,387,388,389,384,376,375,377,372,373,374,368,367,369,370,371,366,482,481,483,484,485,480,395,394,390,391,392,393,383,382,378,379,380,381,116,115,114,119,117,118,165,166,167,164,162,163,108,110,109,111,112,113,232,231,233,228,229,230,102,104,103,106,107,105,256,255,257,253,254,252,94,93,95,91,92,90,100,99,101,97,98,96,201,203,202,198,199,200,552,542,527,532,516,522,548,511,537,563,578,588,583,568,573,558,430,429,431,427,426,428,278,276,279,280,281,277,290,289,291,292,293,288,298,297,299,294,295,296,453,452,454,455,450,451,282,287,283,284,285,286,302,301,303,304,305,300,3,5,4,1,0,2,179,174,175,176,177,178,20,19,18,23,21,22,213,215,214,212,211,210,27,29,28,25,26,24,245,244,243,242,241,240,17,16,15,14,12,13,9,11,10,6,7,8,183,185,184,181,180,182,554,544,529,534,519,524,549,514,539,565,580,590,585,570,574,560,473,472,468,469,470,471,342,347,343,344,345,346,353,352,348,349,350,351,356,355,357,358,359,354,476,475,477,478,479,474,339,338,340,341,336,337,363,362,364,365,360,361,61,60,62,64,65,63,83,82,81,79,80,78,85,84,86,88,89,87,226,225,227,222,223,224,170,168,169,171,172,173,268,267,269,264,266,265,76,75,77,73,74,72,66,68,67,69,70,71,196,195,197,193,194,192,553,543,528,533,518,523,546,510,538,564,579,589,584,569,575,559,458,457,459,460,461,456,315,314,316,317,312,313,310,309,311,306,307,308,333,332,334,335,330,331,462,467,463,464,465,466,323,322,318,319,320,321,324,329,325,326,327,328,40,39,41,37,38,36,45,47,46,44,42,43,159,161,160,157,156,158,216,218,217,221,219,220,50,49,48,51,52,53,246,248,247,249,250,251,54,56,55,57,58,59,34,33,35,31,32,30,189,191,190,186,187,188,551,541,526,531,515,520,545,513,536,562,577,587,581,567,572,557,487,486,488,489,490,491,407,406,402,403,404,405,409,408,410,411,412,413,418,417,419,414,415,416,496,495,497,492,493,494,398,397,399,400,401,396,423,422,424,425,420,421,125,124,123,122,120,121,141,143,142,140,138,139,150,152,151,153,154,155,239,238,237,235,236,234,146,145,144,147,148,149,259,258,260,262,263,261,137,136,135,134,132,133,127,126,128,130,131,129,205,204,209,207,208,206,550,540,525,530,517,521,547,512,535,561,576,586,582,566,571,556 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#b1cd85d3b2010871ff4296ca3922edaff9632ccb3821306d9c0360a13ac5958c, M = the submagma generated by {0, 6} (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 2026-10-07 07:36:28 · history