Equation 677 Database

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Magma fa3272d2b8bb…

magma fa3272d2b8bb
Size
595
Isomorphism class hash
fa3272d2b8bb26a1926b19770f42f026b8658656c414f89566c1739becae0b6f
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 04:54:59
Display reorder
27,118,81,44,22,119,82,45,23,120,77,40,24,121,78,41,25,122,79,42,26,123,80,43,64,66,67,68,63,65,513,510,523,511,512,237,224,249,288,283,291,294,15,108,53,17,166,177,200,178,183,167,55,33,85,154,284,292,295,215,259,234,216,444,441,456,442,436,395,388,405,429,427,431,433,383,410,54,16,184,176,202,179,165,56,34,86,155,151,159,160,332,353,339,333,366,364,370,322,297,236,223,248,289,285,293,296,214,260,235,323,326,365,374,373,360,340,335,347,430,428,432,434,382,411,394,462,463,440,464,461,582,580,515,546,516,543,514,522,519,550,554,590,594,589,560,564,494,482,472,477,480,503,475,414,406,426,435,443,377,409,279,271,305,272,243,217,225,58,174,31,116,87,150,164,128,3,104,141,182,130,76,218,226,238,301,222,264,250,498,501,493,467,489,496,505,418,402,384,390,396,438,387,117,88,148,162,129,4,105,142,180,131,74,18,39,57,173,32,115,89,149,163,127,5,103,139,181,132,75,19,336,341,363,334,354,348,357,161,270,2,257,140,520,517,572,557,535,573,528,526,540,566,563,548,552,567,562,549,152,172,157,97,47,133,112,239,319,275,255,252,246,213,107,111,91,153,171,158,98,227,273,262,240,320,276,256,261,247,212,258,251,286,299,156,96,48,134,113,59,199,137,101,109,84,14,106,90,287,300,290,253,228,274,263,481,509,495,488,492,484,471,490,485,499,502,500,486,478,135,114,60,198,136,102,110,346,331,352,349,358,362,359,408,392,419,413,397,455,420,487,412,404,381,491,592,591,579,529,556,581,542,545,531,525,578,585,539,559,537,583,506,466,483,469,479,504,470,473,508,497,474,468,507,476,361,350,328,369,327,345,329,51,175,13,21,195,143,28,93,192,35,168,6,188,0,244,205,232,303,209,220,317,144,29,94,193,36,169,7,310,204,245,206,233,302,210,20,196,145,30,95,194,37,170,8,189,1,83,9,52,439,380,385,454,423,386,407,453,389,437,378,448,376,403,207,231,304,211,219,318,280,221,92,197,38,298,584,586,587,558,524,538,571,588,536,527,575,533,518,534,577,555,306,266,241,282,315,267,311,187,138,49,100,11,70,201,71,73,12,185,125,61,146,316,268,312,308,277,230,254,391,400,457,401,379,445,415,398,425,452,416,449,447,421,50,99,46,69,203,72,10,186,124,62,147,191,126,190,368,356,338,351,337,343,371,321,208,309,265,242,281,314,269,313,307,278,229,325,324,344,375,372,330,367,355,342,424,451,417,450,446,422,393,460,459,399,465,458,574,576,568,565,570,551,569,553,561,530,532,541,593,521,544,547 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, 1} (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 04:55:05 · history