Equation 677 Database

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Magma d6aa03a37840…

magma d6aa03a37840
Size
595
Isomorphism class hash
d6aa03a37840606ce017aadb791288bc2ea5381d13b3cd1227549c40385e28cb
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
2026-10-06 08:19:01
Display reorder
270,271,272,275,273,274,280,279,281,276,278,277,367,366,368,369,370,371,505,509,504,506,507,508,374,373,375,376,377,372,556,555,594,582,593,218,216,221,219,220,217,76,75,74,71,72,73,77,79,78,80,81,82,88,87,86,85,83,84,68,70,69,65,66,67,26,25,24,27,28,29,199,200,198,201,202,203,207,209,208,204,206,205,255,257,256,254,252,253,378,383,379,380,381,382,312,317,313,314,315,316,393,392,394,395,390,391,323,322,318,319,320,321,307,306,308,309,310,311,401,400,396,397,398,399,386,385,387,388,389,384,524,549,529,533,539,518,554,519,544,565,592,576,561,571,581,587,227,225,224,222,223,226,122,124,123,119,121,120,12,14,13,15,16,17,2,0,1,5,3,4,135,134,136,132,133,131,44,43,42,45,46,47,6,8,7,9,10,11,91,90,89,92,93,94,263,262,261,259,260,258,442,441,443,438,439,440,359,358,354,355,356,357,408,413,409,410,411,412,363,362,364,365,360,361,348,353,349,350,351,352,404,403,405,406,407,402,436,435,437,432,433,434,520,546,526,532,535,510,553,513,543,564,591,575,557,567,580,583,238,239,235,236,234,237,100,99,98,95,96,97,109,108,107,112,110,111,117,116,118,114,115,113,37,36,38,40,41,39,125,127,126,129,130,128,103,102,101,106,104,105,178,177,176,173,174,175,249,251,250,248,246,247,342,347,343,344,345,346,425,424,420,421,422,423,470,469,471,472,467,468,429,428,430,431,426,427,414,419,415,416,417,418,475,474,476,477,478,473,336,341,337,338,339,340,523,545,527,531,537,512,550,511,540,566,588,573,559,570,577,584,211,210,213,214,215,212,64,63,62,60,61,191,51,53,52,48,49,50,56,55,54,59,57,58,140,142,141,137,138,139,22,21,23,20,18,19,197,196,195,194,192,193,190,189,188,185,186,187,268,267,269,264,265,266,446,445,447,448,449,444,298,297,299,294,295,296,500,499,501,502,497,498,302,301,303,304,305,300,293,292,288,289,290,291,286,285,287,283,282,284,452,451,453,454,455,450,521,547,525,534,538,516,551,515,542,562,589,572,558,568,578,585,229,230,232,233,231,228,163,162,161,164,165,166,149,151,150,152,153,154,160,159,158,157,155,156,31,30,32,34,35,33,179,181,180,183,184,182,171,170,172,168,169,167,144,143,145,148,146,147,240,241,242,243,244,245,333,332,334,335,330,331,487,486,488,489,490,485,463,466,464,465,462,503,491,496,492,493,494,495,482,481,483,484,479,480,459,458,460,461,456,457,327,326,328,329,324,325,522,548,528,530,536,514,552,517,541,563,590,574,560,569,579,586 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#21508ce76d8339c8cc8a9db508194b7933fb8eb19570d11d640cb6bc14178d14, M = the submagma generated by {18, 54} (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 2026-10-06 08:19:02 · history