Equation 677 Database

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Magma 290167b6a06f…

magma 290167b6a06f
Size
595
Isomorphism class hash
290167b6a06f4b843756d35f38e939e93bc5b866f66f2a943c4fc5286fda42f2
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 13:18:58
Display reorder
73,76,74,75,72,77,107,106,108,103,104,105,336,338,337,340,341,339,472,471,473,468,469,470,423,425,424,422,420,421,523,533,531,564,563,255,258,162,256,257,201,192,135,136,132,133,134,117,116,118,119,114,115,99,102,100,237,238,101,240,241,193,194,148,149,165,164,166,167,168,266,208,267,209,268,206,207,231,185,232,186,230,184,179,24,20,21,22,23,344,343,342,347,345,346,495,497,496,493,492,494,396,398,397,401,399,400,467,466,465,463,464,462,498,500,499,503,501,502,409,408,410,411,412,413,441,443,442,439,440,438,540,546,534,536,532,535,526,574,573,578,562,551,592,554,553,589,43,42,44,45,46,47,5,4,0,1,2,3,57,56,58,59,60,55,19,18,14,15,16,17,125,124,120,121,122,123,62,61,63,64,65,229,243,157,244,245,196,195,222,221,31,223,224,180,189,85,81,82,83,84,385,384,386,388,389,387,430,429,431,427,428,426,395,394,393,391,392,390,452,451,450,454,455,453,324,326,325,329,327,328,478,477,479,475,474,476,504,509,506,508,505,507,539,527,510,522,516,513,547,548,556,570,576,584,579,582,581,569,13,12,8,9,10,11,28,27,29,30,25,26,91,90,92,87,88,89,95,94,96,97,98,93,36,35,37,32,33,34,110,113,111,112,109,274,280,169,281,277,272,273,276,278,150,279,275,242,239,140,141,137,138,139,458,457,456,461,459,460,288,290,289,291,292,293,365,364,363,361,362,360,315,317,316,314,312,313,351,353,352,350,348,349,485,484,483,480,482,481,306,308,307,310,311,309,538,542,519,525,520,521,524,550,565,566,560,594,568,575,580,558,129,128,130,131,126,127,86,236,191,234,190,235,172,171,215,173,214,170,227,181,182,48,49,50,40,39,41,38,225,226,158,247,246,198,197,269,211,271,213,270,210,212,261,204,259,202,260,203,205,265,262,163,263,264,366,368,367,369,370,371,330,332,331,333,334,335,323,322,321,319,320,318,414,416,415,419,417,418,355,354,356,357,358,359,382,381,383,378,379,380,377,376,375,372,373,374,541,545,529,528,530,518,512,567,559,571,561,593,586,591,590,572,68,67,69,70,71,66,159,249,250,160,251,248,175,174,216,217,6,218,233,187,188,79,80,78,52,51,53,54,183,228,219,220,176,177,178,7,154,153,155,156,151,152,142,147,143,144,145,146,161,200,252,253,254,199,300,302,301,303,304,305,402,404,403,405,406,407,295,294,296,297,298,299,436,435,437,432,433,434,491,490,489,486,488,487,282,283,284,285,286,287,446,445,444,447,448,449,537,543,511,514,515,517,544,587,585,557,555,583,549,588,577,552 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#3cc60f474fc5309f8bfdc916c4fdc0ad032cdecf3f770b83999110b499ecb4f1, M = the submagma generated by {6, 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 2026-10-07 13:18:59 · history