Equation 677 Database

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Magma 5d4442cb5772…

magma 5d4442cb5772
Size
595
Isomorphism class hash
5d4442cb5772e04c427ff07dc093b8ba70d99e93d427c8b71868885e0e437951
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 07:13:42
Display reorder
96,95,97,92,93,94,45,44,40,41,42,43,156,155,157,152,153,154,405,407,406,402,403,404,494,492,493,497,495,496,514,523,571,549,582,277,276,174,274,275,219,195,121,122,123,124,120,133,132,134,135,136,131,145,144,146,243,242,143,245,246,198,199,150,151,25,29,26,27,28,225,210,261,211,260,208,209,233,190,234,191,232,189,186,63,59,60,61,62,369,371,370,367,368,366,339,341,340,337,338,336,499,498,500,503,501,502,400,399,401,398,396,397,356,355,354,358,359,357,434,433,432,435,436,437,448,447,449,444,445,446,518,545,535,536,532,521,534,572,579,581,556,557,588,593,570,574,2,1,4,5,0,3,16,15,17,12,13,14,58,57,53,54,55,56,114,119,115,116,117,118,50,49,51,46,47,48,110,109,111,112,113,241,231,64,229,230,187,188,268,267,168,265,266,216,194,102,98,99,100,101,462,464,463,466,467,465,470,469,468,471,472,473,421,420,422,425,423,424,416,415,414,417,418,419,508,507,509,504,505,506,411,413,412,409,410,408,490,489,491,486,487,488,530,531,512,513,511,510,546,547,569,575,565,591,553,552,566,576,106,105,108,103,104,107,23,22,24,19,20,21,88,87,89,84,85,86,9,8,10,11,6,7,125,130,126,127,128,129,78,77,75,76,74,280,286,175,287,283,278,279,281,285,167,284,282,262,236,82,83,79,80,81,310,309,311,308,306,307,393,395,394,391,392,390,299,298,297,294,295,296,375,377,376,373,374,372,361,360,362,363,364,365,302,301,300,303,304,305,330,332,331,335,333,334,537,538,522,517,519,516,520,578,559,573,561,589,594,564,560,562,163,162,159,160,161,158,18,223,181,224,180,222,176,177,220,178,221,179,244,196,197,147,148,149,171,170,169,173,272,269,172,273,270,217,218,271,214,263,215,264,212,213,254,205,255,203,256,204,202,253,250,165,251,252,454,453,455,452,450,451,317,316,315,312,313,314,319,318,320,323,321,322,384,386,385,388,389,387,478,475,474,477,479,476,460,459,461,458,456,457,324,326,325,329,327,328,540,544,526,529,528,525,515,568,580,592,551,586,590,583,585,563,32,31,34,35,30,33,90,238,239,91,240,237,201,200,249,247,164,248,235,192,193,73,71,72,37,36,38,39,182,226,228,227,185,183,184,52,140,139,141,142,137,138,66,65,67,68,69,70,166,207,257,258,259,206,353,352,351,348,349,350,347,346,345,342,343,344,431,430,429,426,427,428,480,482,481,484,485,483,289,290,288,293,291,292,380,379,378,381,382,383,441,443,442,440,438,439,533,527,541,542,524,539,543,567,558,554,550,555,577,548,587,584 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#83fb73755ed07f789756511d0e776415c2bd28bb0aaa387c6c265081499d5ced, M = the submagma generated by {18, 30} (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 07:13:45 · history