Equation 677 Database

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Magma 93a6a3f36f0c…

magma 93a6a3f36f0c
Size
595
Isomorphism class hash
93a6a3f36f0c6acadfc3cced3030267378cc0418a6cc91f5414df1fa95d24cce
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 16:44:26
Display reorder
300,301,302,304,305,303,315,314,316,317,312,313,320,319,321,322,323,318,308,306,309,310,311,307,508,507,509,505,504,506,555,593,594,581,582,171,173,172,168,169,170,142,141,143,140,138,139,164,163,162,166,167,165,257,256,255,252,254,253,287,286,285,284,282,283,263,262,261,258,260,259,144,146,145,147,148,149,71,70,69,66,67,68,152,151,150,153,154,155,161,160,159,156,157,158,408,413,409,410,411,412,343,342,344,345,346,347,348,353,349,350,351,352,415,414,416,417,418,419,482,481,483,484,485,480,403,402,404,405,406,407,532,520,540,552,537,519,513,548,527,558,565,580,568,573,585,590,126,128,127,129,130,131,36,35,34,37,38,39,115,114,116,117,118,119,123,125,124,122,120,121,279,281,280,276,277,278,40,42,41,45,43,44,27,28,46,24,25,26,136,135,137,134,132,133,31,33,32,29,30,47,246,247,248,251,249,250,380,379,381,382,383,378,395,394,390,391,392,393,400,399,401,396,397,398,472,471,473,469,468,470,492,497,493,494,495,496,384,389,385,386,387,388,531,517,544,550,535,516,512,547,526,556,564,578,567,574,584,589,50,49,48,53,51,52,194,193,192,195,196,197,55,54,56,57,58,59,220,219,221,217,216,218,288,290,289,291,292,293,177,179,178,176,174,175,181,180,182,184,185,183,266,264,265,267,268,269,186,188,187,190,191,189,198,200,199,202,203,201,437,436,432,433,434,435,430,429,431,426,427,428,422,421,423,424,425,420,326,325,327,328,329,324,501,500,502,503,498,499,441,440,442,443,438,439,534,524,541,553,539,521,510,546,525,560,562,576,570,572,587,591,93,95,94,90,91,92,105,107,106,103,104,102,231,233,232,230,229,228,84,86,85,89,87,88,273,275,274,271,270,272,111,113,112,110,108,109,227,226,225,224,223,222,81,83,82,79,80,78,100,99,101,98,96,97,72,74,73,76,77,75,356,355,357,358,359,354,369,368,370,371,366,367,374,373,375,376,377,372,462,463,464,465,466,467,490,489,491,486,487,488,360,365,361,362,363,364,533,518,543,554,538,522,511,549,528,559,561,577,569,571,586,592,208,207,209,205,206,204,3,5,4,0,2,1,235,236,234,239,237,238,243,245,244,242,241,240,295,294,296,298,299,297,7,6,8,9,10,11,13,12,14,16,17,15,61,60,62,65,63,64,21,23,22,19,20,18,214,213,215,212,210,211,451,450,452,453,454,455,338,337,339,340,341,336,331,330,332,333,334,335,447,446,448,449,444,445,477,476,478,479,475,474,461,460,456,457,458,459,530,523,542,551,536,515,514,545,529,557,563,579,566,575,583,588 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#fc7d721c9159906f161771735410c214fae4809487be4161a48baf4a48d744a1, M = the submagma generated by {18, 78} (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 16:44:27 · history