Equation 677 Database

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Magma 1a0d6283c055…

magma 1a0d6283c055
Size
595
Isomorphism class hash
1a0d6283c05525e53d788fdc3cb42e611d764bd5ce7b288a869800ef27118767
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 09:59:39
Display reorder
68,66,71,69,70,67,158,157,156,159,160,161,116,115,114,117,118,119,385,384,386,387,388,389,414,419,415,416,417,418,529,536,519,572,570,170,169,168,171,172,173,34,33,32,31,29,30,95,94,93,90,91,92,65,12,13,15,16,14,191,187,195,183,256,253,238,237,249,239,240,241,210,212,211,208,248,209,147,149,148,145,146,144,426,431,427,428,429,430,359,358,354,355,356,357,452,451,453,454,455,450,369,368,370,371,366,367,392,391,393,394,395,390,276,281,277,278,279,280,265,264,266,267,268,269,473,472,468,469,470,471,518,534,551,546,514,538,543,525,573,577,579,593,592,566,562,565,207,206,205,202,203,204,246,245,247,243,244,242,251,255,182,192,184,188,86,85,84,89,87,88,51,50,52,49,47,48,150,152,151,154,155,153,179,178,177,176,174,175,222,224,223,220,221,219,422,421,423,424,425,420,462,467,463,464,465,466,434,433,435,436,437,432,504,509,505,506,507,508,474,479,475,476,477,478,412,411,413,408,409,410,459,458,460,461,456,457,299,298,294,295,296,297,524,548,535,539,552,544,517,542,586,571,583,588,580,590,560,582,27,26,28,25,23,24,0,1,2,4,5,3,45,44,46,43,41,42,8,7,6,11,9,10,17,19,18,21,22,20,133,132,134,137,135,136,40,39,38,37,35,36,83,82,81,78,79,80,442,441,443,438,439,440,495,494,496,497,492,493,498,503,499,500,501,502,305,304,300,301,302,303,491,490,486,487,488,489,319,318,320,321,322,323,343,342,344,345,346,347,396,401,397,398,399,400,510,523,532,515,511,512,513,516,594,558,555,578,568,569,567,585,230,229,228,225,226,227,215,214,213,218,216,217,252,257,181,194,186,190,56,58,57,53,54,55,113,112,111,108,109,110,140,139,138,141,142,143,167,166,165,164,162,163,122,121,120,123,124,125,383,382,378,379,380,381,341,340,336,337,338,339,405,404,406,407,402,403,282,287,283,284,285,286,271,270,272,273,274,275,307,306,308,309,310,311,292,291,293,288,289,290,446,445,447,448,449,444,521,530,533,537,547,549,528,541,591,557,554,574,576,556,581,575,97,96,98,101,99,100,129,131,130,126,127,128,61,60,59,62,63,64,75,77,76,72,73,74,189,185,193,180,254,250,235,234,236,233,231,232,198,197,196,201,199,200,104,103,102,105,106,107,325,324,326,327,328,329,482,481,483,484,485,480,353,352,348,349,350,351,258,259,260,261,262,263,372,377,373,374,375,376,362,361,363,364,365,360,317,316,312,313,314,315,333,332,334,335,330,331,520,527,550,545,531,526,540,522,553,563,561,559,584,564,589,587 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#fd7de578af0812c41995e8ffd4ad83dcb5427b7eb760f7a58401ca67989e247a, M = the submagma generated by {0, 36} (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 09:59:40 · history