Equation 677 Database

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Magma 2957f2b4e290…

magma 2957f2b4e290
Size
595
Isomorphism class hash
2957f2b4e290fd6ea8c3cb500afc431d653b3b726bac071fed275b4a00f683a5
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 13:52:16
Display reorder
82,78,77,80,81,79,56,55,51,52,53,54,140,139,141,136,137,138,44,43,39,40,41,42,476,478,477,474,475,479,524,570,563,586,565,249,248,180,250,251,247,156,6,7,8,9,10,73,72,68,69,70,71,58,57,59,196,197,163,204,203,205,165,60,61,148,147,149,146,150,241,176,242,238,239,240,177,229,228,230,174,226,227,380,379,378,383,381,382,268,267,269,264,266,265,493,492,494,496,497,495,364,363,365,362,360,361,434,433,432,437,435,436,487,486,488,489,490,491,450,452,451,454,455,453,467,466,465,463,464,462,548,547,539,530,538,528,532,531,593,553,568,566,591,569,551,552,3,2,4,5,0,1,115,114,116,117,112,113,105,104,100,101,102,103,107,106,108,109,110,111,123,122,118,119,120,121,87,86,83,84,85,208,221,171,222,219,220,170,233,237,175,234,235,236,504,499,498,502,500,501,343,342,344,346,347,345,390,392,391,393,394,395,304,303,305,302,300,301,509,507,506,508,505,503,275,274,273,271,272,270,355,354,356,359,357,358,314,313,312,316,317,315,529,527,521,550,549,520,519,515,554,576,574,573,579,580,590,584,92,91,93,88,89,90,27,26,28,23,24,25,14,13,15,16,11,12,17,22,18,19,20,21,94,99,95,96,97,98,152,151,153,154,155,263,258,252,255,256,257,185,261,254,253,262,260,259,297,299,298,294,295,296,438,440,439,441,442,443,430,429,431,427,428,426,286,285,287,284,282,283,384,386,385,387,388,389,418,417,419,414,415,416,446,445,444,447,448,449,308,307,306,310,311,309,535,533,518,514,512,516,517,513,571,559,556,555,594,572,589,588,37,36,38,33,34,35,124,216,213,214,169,215,209,168,210,167,211,212,190,191,160,30,31,32,143,142,144,145,231,232,179,243,245,246,178,244,162,192,193,194,195,161,198,202,199,164,200,201,399,401,400,396,397,398,413,412,411,410,408,409,460,459,461,457,458,456,473,472,471,468,469,470,406,405,407,403,404,402,328,327,329,324,325,326,337,336,338,341,339,340,481,480,484,483,485,482,544,546,523,522,510,526,534,511,558,582,562,575,592,587,561,581,47,46,48,49,50,45,29,189,186,159,187,188,182,158,183,184,157,181,207,206,166,75,76,74,126,125,127,128,218,217,225,224,172,223,173,135,129,134,130,131,132,133,63,62,64,65,66,67,293,292,291,290,288,289,425,424,423,422,420,421,366,368,367,369,370,371,353,352,351,348,349,350,276,278,277,279,280,281,331,330,332,333,334,335,375,377,376,373,374,372,318,320,319,323,321,322,540,541,536,545,543,525,542,537,560,557,567,578,577,583,564,585 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#7c5787f3763007370795fcf378d2af7959e084037efbb89592fd99450acc2142, M = the submagma generated by {0, 12} (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 13:52:18 · history