Equation 677 Database

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Magma c260ea85ced9…

magma c260ea85ced9
Size
595
Isomorphism class hash
c260ea85ced945ecad01647d94df1dcaf1b5e6a0c7ac49e90272e23272069dee
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 08:08:34
Display reorder
68,26,44,48,66,27,42,49,67,28,43,50,71,29,41,51,69,30,39,52,70,31,40,53,10,11,15,13,14,12,511,510,512,514,513,505,508,504,503,509,507,506,457,463,468,486,456,469,472,229,193,232,197,236,206,198,183,158,156,126,145,148,179,307,311,285,302,303,287,310,354,344,406,380,376,347,369,371,405,379,381,334,372,346,308,299,301,320,288,304,309,133,123,182,155,150,119,160,77,74,82,16,58,72,113,122,153,159,132,124,180,151,0,78,86,83,17,75,59,277,284,271,278,279,273,272,181,117,149,116,161,585,586,579,572,580,574,575,578,573,522,518,519,526,565,525,515,91,106,94,98,101,109,54,104,62,112,111,57,65,108,488,487,473,462,482,474,477,478,483,459,481,465,485,484,225,260,266,268,241,222,256,164,166,168,176,144,170,146,451,450,447,449,452,453,448,316,300,319,318,298,312,313,163,165,167,143,186,185,175,276,274,281,280,275,283,282,221,240,255,244,246,249,267,265,226,259,261,252,219,224,404,400,368,384,393,385,386,387,325,408,332,397,530,529,537,535,545,569,568,564,532,558,560,557,587,588,559,556,495,498,501,500,499,493,492,455,476,467,480,461,470,454,210,202,223,220,235,247,242,90,34,21,9,97,64,103,81,3,20,35,60,56,85,248,243,237,209,203,195,245,496,502,497,489,491,494,490,458,475,466,479,460,464,471,99,92,89,23,36,19,4,80,24,32,8,95,63,102,55,61,84,100,93,87,37,18,79,5,33,7,22,96,324,330,322,323,327,329,328,88,157,211,130,6,590,589,527,531,541,533,534,540,536,520,542,567,517,563,521,516,46,45,2,110,107,47,38,251,227,263,213,218,270,201,128,190,138,141,136,120,177,173,140,134,169,147,178,135,191,127,192,129,139,142,137,194,262,257,217,212,250,228,401,359,413,349,414,350,388,427,429,440,423,428,425,424,339,399,394,357,351,415,348,416,358,366,389,370,402,361,297,295,294,286,317,314,291,445,446,420,426,434,422,430,403,360,367,363,362,338,398,315,418,352,417,290,577,576,549,562,543,523,566,544,524,546,539,582,593,538,581,594,25,76,73,115,1,114,105,269,254,205,200,215,231,238,343,395,356,364,378,373,412,333,407,392,409,390,353,345,230,239,258,196,208,214,234,154,189,118,184,172,188,171,131,125,152,162,174,121,187,264,253,204,199,216,207,233,375,411,337,391,342,396,383,432,437,441,444,435,421,419,365,355,377,374,410,335,340,439,431,433,442,443,438,436,292,289,296,293,306,305,321,336,326,341,331,382,570,571,555,592,591,552,561,553,554,551,583,547,550,584,528,548 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#a8026a02368cc98eace7a76910bb242dec082e21ec6371f1fc7226b87fb07666, M = the submagma generated by {9, 10} (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 08:08:35 · history