Equation 677 Database

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Magma 8b9800a6979a…

magma 8b9800a6979a
Size
595
Isomorphism class hash
8b9800a6979a3467966c59db7e39cd868900fb861521ee7fa0af1a80c13067c5
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 19:52:03
Display reorder
285,284,286,287,282,283,500,498,501,502,503,499,505,509,504,506,507,508,281,280,277,276,278,279,271,272,270,275,273,274,520,593,586,587,594,450,455,451,452,453,454,480,482,481,484,485,483,465,464,466,467,462,463,473,472,468,469,470,471,459,458,460,461,456,457,489,488,490,491,486,487,479,478,474,475,476,477,84,86,85,87,88,89,137,136,135,132,133,134,175,176,174,178,179,177,269,268,267,265,266,264,170,172,171,168,173,169,236,235,234,238,239,237,94,93,95,90,91,92,128,127,126,131,129,130,204,205,206,207,208,209,527,535,514,519,525,555,540,545,550,592,584,570,575,580,565,560,395,394,390,391,392,393,377,373,372,375,376,374,384,389,385,386,387,388,331,330,332,333,334,335,378,383,379,380,381,382,369,368,370,371,366,367,337,336,338,339,340,341,45,47,46,42,43,44,157,158,156,160,161,159,165,167,166,162,164,163,249,251,250,248,246,247,97,96,98,100,101,99,225,227,226,224,222,223,37,36,38,39,40,41,48,50,49,51,52,53,202,201,203,199,198,200,529,533,513,518,522,554,539,544,549,591,581,569,573,579,563,559,494,493,495,496,497,492,405,407,406,403,404,402,419,418,414,415,416,417,344,343,345,346,347,342,412,411,413,408,409,410,399,398,400,401,396,397,350,349,351,352,353,348,56,55,54,59,57,58,104,103,102,105,106,107,61,60,62,65,63,64,254,253,252,256,257,255,113,112,111,110,108,109,233,232,231,229,230,228,71,70,69,67,68,66,77,76,75,74,72,73,192,194,193,197,195,196,526,532,510,516,523,552,537,542,547,589,585,566,571,576,562,557,437,436,432,433,434,435,355,357,356,359,354,358,446,445,447,448,449,444,428,427,429,430,431,426,440,439,441,442,443,438,364,363,365,360,361,362,422,421,423,424,425,420,2,0,1,5,3,4,79,78,80,83,81,82,7,6,8,11,9,10,260,259,258,262,263,261,122,121,120,125,123,124,220,219,221,216,217,218,141,143,142,140,139,138,119,118,117,116,114,115,181,182,180,185,183,184,524,534,511,515,530,553,536,541,546,588,582,567,574,577,564,556,314,313,315,316,317,312,324,326,325,328,329,327,309,308,310,311,306,307,291,290,292,293,288,289,303,302,304,305,300,301,320,319,321,322,323,318,299,298,294,295,296,297,23,22,21,20,18,19,148,147,149,146,145,144,155,154,153,151,150,152,245,244,243,240,242,241,34,33,35,31,32,30,212,210,211,214,215,213,24,26,25,29,27,28,14,13,12,17,15,16,191,190,189,187,188,186,528,531,512,517,521,551,538,543,548,590,583,568,572,578,561,558 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#20e9cec11ce1b4ef3a4be2ce0eb77a027f26009c155c08499f343b203c8ba1b3, M = the submagma generated by {18, 30} (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 19:52:04 · history