Equation 677 Database

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Magma e2c40991987f…

magma e2c40991987f
Size
595
Isomorphism class hash
e2c40991987f4e0431a777862c4f4d47ffa4d43b7d21c8010e15f7b6fb0c8c78
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 09:23:24
Display reorder
395,394,390,391,392,393,507,506,508,509,505,504,416,415,417,418,419,414,377,376,372,373,374,375,272,270,271,275,273,274,555,576,577,594,593,497,492,493,494,495,496,482,481,483,484,485,480,303,302,304,305,300,301,294,299,295,296,297,298,293,292,288,289,290,291,470,469,471,472,473,468,285,284,286,287,282,283,29,31,30,32,33,34,120,119,121,122,123,124,236,235,234,238,239,237,185,184,183,180,182,181,40,39,38,36,37,35,28,27,26,24,25,23,126,125,127,128,129,130,143,145,144,148,146,147,216,218,217,219,220,221,541,530,513,515,535,525,547,550,521,560,571,567,562,578,589,584,396,397,398,399,400,401,345,344,346,347,342,343,330,335,331,332,333,334,450,455,451,452,453,454,383,382,378,379,380,381,502,501,503,498,499,500,486,491,487,488,489,490,149,151,150,152,153,154,22,21,20,18,19,17,215,214,213,210,212,211,199,201,200,198,196,197,159,161,160,158,157,156,134,136,135,133,131,132,66,65,67,68,69,70,99,98,100,95,96,97,225,227,226,222,223,224,540,532,510,516,537,526,545,551,522,556,572,566,561,579,588,583,437,432,433,434,435,436,365,364,360,361,362,363,429,428,430,431,426,427,371,370,366,367,368,369,306,311,307,308,309,310,356,355,357,358,359,354,424,423,425,420,421,422,108,107,109,111,112,110,167,166,165,162,164,163,228,230,229,233,231,232,208,186,187,188,209,189,103,102,101,105,106,104,78,77,79,80,81,82,83,85,84,88,86,87,46,45,44,42,43,41,264,266,265,267,268,269,542,531,511,519,539,527,546,552,524,559,573,568,563,580,590,585,410,411,412,413,408,409,313,312,314,315,316,317,385,384,386,387,388,389,479,478,474,475,476,477,322,321,323,318,319,320,325,324,326,327,328,329,446,445,447,448,449,444,64,63,62,61,59,60,57,56,58,53,54,55,259,258,260,261,262,263,204,203,202,206,207,205,171,173,172,170,169,168,92,94,93,91,89,90,47,49,48,52,50,51,8,10,9,7,5,6,248,247,246,251,249,250,543,533,512,518,538,529,549,553,523,558,574,570,565,581,591,586,341,336,337,338,339,340,466,465,467,462,463,464,405,404,406,407,402,403,277,281,276,278,279,280,461,460,456,457,458,459,441,440,442,443,438,439,350,349,351,352,353,348,117,116,118,114,115,113,71,73,72,76,74,75,245,244,243,241,242,240,193,195,194,192,190,191,174,176,175,179,177,178,142,141,140,138,139,137,155,0,1,4,2,3,15,14,16,11,12,13,255,257,256,252,253,254,544,534,514,517,536,528,548,554,520,557,575,569,564,582,592,587 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#5ad34b2f8758383b4965947b4701d5813e2a88f030dcc851453e9c1dba339352, M = the submagma generated by {0, 12} (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 09:23:25 · history