Equation 677 Database

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Magma 6bd1d738d9a7…

magma 6bd1d738d9a7
Size
595
Isomorphism class hash
6bd1d738d9a7dbba7627b2c76109a4cf72e087487e577f2f2b0a2783b6a74ea7
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 20:54:23
Display reorder
102,52,38,30,76,103,53,39,31,77,104,54,40,32,78,99,49,35,27,79,100,50,36,28,80,101,51,37,29,81,511,512,515,510,513,219,301,236,216,220,222,253,70,92,56,82,121,116,23,163,122,34,169,64,25,41,223,254,240,255,233,246,295,416,388,418,391,434,399,390,392,393,411,402,412,395,407,164,117,24,120,33,168,63,26,42,43,91,71,93,55,346,364,351,331,353,333,369,235,217,221,224,252,241,256,232,245,296,266,215,269,218,368,341,332,334,335,348,343,413,396,406,432,417,389,456,465,460,454,459,463,520,521,580,582,581,579,583,578,584,536,565,542,552,547,564,594,486,492,477,474,499,489,468,387,441,405,380,379,378,431,284,206,280,289,259,248,306,141,14,19,184,74,10,138,3,162,7,132,147,96,86,305,287,210,213,311,244,207,487,466,496,467,485,491,476,410,438,426,383,386,442,404,8,136,4,160,5,133,148,97,87,179,142,12,17,185,75,9,137,2,161,6,134,149,98,85,178,143,13,18,373,345,328,359,327,363,355,127,273,125,272,126,556,557,569,534,529,566,533,523,530,538,546,540,545,526,527,543,109,20,107,47,112,118,45,298,277,325,321,320,316,317,201,196,110,21,105,48,113,267,228,297,278,326,322,323,315,318,319,261,214,260,230,114,119,46,165,129,203,198,199,190,192,194,111,22,106,231,262,268,229,299,276,324,506,507,504,503,505,479,469,478,471,480,482,470,497,484,202,197,200,193,191,195,108,330,349,338,350,352,337,365,421,449,447,448,445,446,450,508,451,452,453,509,549,550,561,539,541,555,592,560,554,589,585,586,587,588,590,591,494,472,495,502,483,488,500,501,493,481,475,498,473,490,371,372,361,340,362,375,356,139,180,182,152,115,95,174,67,144,175,155,60,158,188,274,285,307,309,292,263,258,173,68,145,176,156,61,159,314,275,286,308,310,293,264,94,172,69,146,177,154,62,157,189,128,140,181,183,153,415,414,436,401,427,437,429,398,430,444,420,425,439,440,294,265,257,304,239,288,249,251,88,89,90,250,568,567,573,577,571,576,572,574,575,528,559,537,531,558,532,553,291,300,237,271,313,282,227,171,15,1,11,58,131,84,72,59,151,167,65,124,187,283,225,303,211,205,208,242,422,408,397,428,433,400,419,443,424,394,435,384,377,381,73,130,83,57,150,166,66,123,186,135,44,170,16,0,329,344,357,347,339,360,367,238,270,312,281,226,302,212,204,209,243,279,247,234,290,366,342,354,374,358,336,370,385,376,382,403,423,409,455,464,461,457,458,462,562,563,544,525,524,570,551,535,548,516,519,517,514,518,522,593 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#ab7663272fb322647e3a6f8af752cc36283f2dfca26817d870d65fdaf95a91e5, M = the submagma generated by {0, 4} (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 20:54:24 · history