Equation 677 Database

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Magma 53544c1b35c3…

magma 53544c1b35c3
Size
595
Isomorphism class hash
53544c1b35c3e8c4f7d12fb2dd69d06afead538a53fb194e16cfef5734f362c9
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 15:19:51
Display reorder
116,115,117,118,119,114,373,372,374,377,375,376,348,347,346,350,351,349,364,363,365,362,360,361,320,319,318,316,317,315,514,510,515,511,552,175,178,176,177,174,179,137,136,132,133,134,135,95,94,90,91,92,93,196,195,197,192,193,194,266,265,267,268,269,264,227,226,222,223,224,225,39,38,40,41,36,37,46,45,47,42,43,44,61,60,62,63,64,65,110,109,111,112,113,108,403,401,402,405,406,404,334,333,332,336,337,335,309,308,310,313,311,312,382,381,383,378,379,380,490,488,508,507,487,489,352,471,437,473,438,472,532,531,522,517,520,518,546,571,576,586,584,550,579,558,549,562,293,290,288,289,292,291,98,97,99,100,101,96,58,57,59,54,55,56,69,68,70,71,66,67,24,29,25,26,27,28,160,159,161,156,157,158,85,84,86,87,88,89,187,186,188,189,190,191,205,204,206,207,208,209,8,7,9,10,11,6,455,454,407,495,501,494,480,500,479,477,478,476,509,493,499,492,452,453,486,449,448,447,445,446,354,356,355,358,359,357,306,463,425,462,424,461,542,529,526,540,541,512,545,580,563,544,590,570,556,547,557,574,102,105,103,104,107,106,31,30,32,33,34,35,240,245,241,242,243,244,215,214,210,211,212,213,202,201,203,198,199,200,13,12,14,15,16,17,144,149,145,146,147,148,140,139,141,142,143,138,217,216,218,219,220,221,180,185,181,182,183,184,411,413,412,410,409,408,393,394,392,397,395,396,343,345,344,341,342,340,326,325,324,322,323,321,483,484,505,391,506,485,469,338,468,504,470,339,536,537,528,525,523,527,581,573,591,572,559,560,561,568,569,589,75,72,76,77,74,73,152,151,153,154,155,150,131,130,126,127,128,129,283,282,284,285,286,287,162,167,163,164,165,166,301,304,305,300,302,303,278,277,279,280,281,276,295,294,296,297,298,299,257,256,252,253,254,255,0,1,2,3,4,5,491,451,450,398,399,400,389,388,387,385,386,384,327,329,328,330,331,436,444,482,390,481,442,443,368,367,366,369,370,371,422,420,502,498,503,421,534,524,535,513,521,543,555,594,593,566,565,592,588,564,551,583,233,230,228,229,232,231,274,273,275,270,271,272,246,251,247,248,249,250,263,262,258,259,260,261,50,49,51,52,53,48,81,80,82,83,78,79,168,173,169,170,171,172,18,23,19,20,21,22,122,121,123,124,125,120,237,236,238,234,239,235,497,456,457,458,459,496,474,439,440,353,441,475,432,431,430,427,428,429,435,467,314,466,434,433,416,415,414,417,418,419,307,460,423,465,426,464,539,538,530,533,519,516,582,585,554,575,577,548,567,587,578,553 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#96b028d3c6de0cbaff964417289f690895c6af42769867ad5a7d2affbed8a752, M = the submagma generated by {0, 66} (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 15:19:52 · history