Equation 677 Database

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Magma e026bafed64e…

magma e026bafed64e
Size
595
Isomorphism class hash
e026bafed64e443a91fa001299ae5c4f26768deafedc547ae410a4ad7af21ec7
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 17:47:16
Display reorder
85,90,86,87,88,89,348,347,349,344,345,346,339,338,340,341,342,343,314,316,315,317,318,319,363,362,364,359,360,361,511,510,512,517,553,268,265,269,264,267,266,203,202,198,199,200,201,220,219,221,216,217,218,65,64,66,61,62,63,92,91,93,94,95,96,283,282,284,285,286,287,122,121,123,124,125,126,281,280,276,277,278,279,9,8,10,11,12,7,14,13,15,16,17,18,389,391,390,394,392,393,413,414,412,415,416,417,388,387,386,384,385,383,353,355,354,357,358,356,466,465,504,505,467,468,404,485,448,483,447,484,533,526,529,527,528,531,555,591,574,560,589,550,578,559,554,587,236,239,237,238,235,234,109,114,110,111,112,113,30,29,25,26,27,28,173,172,174,175,176,177,180,179,181,182,183,178,246,251,247,248,249,250,299,298,294,295,296,297,149,148,195,145,146,147,227,226,222,223,224,225,164,163,165,160,161,162,425,424,306,462,500,463,491,501,492,488,489,490,508,475,499,476,435,436,477,441,437,438,439,440,313,312,311,310,308,309,307,464,426,461,423,460,542,535,541,518,540,519,570,583,562,593,563,569,564,566,579,581,256,253,257,252,255,254,31,36,32,33,34,35,230,229,231,232,233,228,209,208,204,205,206,207,53,52,54,49,50,51,55,60,56,57,58,59,305,304,300,301,302,303,194,193,197,190,191,192,196,1,150,151,152,153,144,143,139,140,141,142,326,328,327,331,329,330,332,334,333,335,336,337,370,372,371,375,373,374,398,400,399,396,397,395,472,471,507,376,506,470,481,403,482,509,480,402,536,537,520,521,515,514,547,549,572,594,573,575,580,590,557,584,48,45,43,44,47,46,244,243,245,240,241,242,37,42,38,39,40,41,0,6,2,3,4,5,83,82,84,79,80,81,167,166,168,169,170,171,158,157,159,154,155,156,189,188,184,185,186,187,104,103,105,106,107,108,292,291,293,288,289,290,469,446,427,351,352,350,410,409,411,406,408,407,367,366,365,368,369,428,454,487,405,486,449,450,379,378,377,382,380,381,422,420,502,498,503,421,534,543,523,516,522,530,552,568,582,565,571,544,545,592,558,546,98,101,99,100,97,102,68,67,69,70,71,72,77,76,78,73,74,75,136,135,137,138,133,134,21,20,22,23,24,19,275,274,270,271,272,273,212,211,213,214,215,210,115,120,116,117,118,119,263,262,258,259,260,261,130,129,131,132,127,128,478,442,443,444,445,479,493,455,456,419,459,497,453,452,451,430,431,429,434,474,401,473,432,433,323,325,324,320,321,322,418,496,458,495,457,494,539,538,524,525,532,513,548,588,567,577,576,561,551,585,586,556 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#92768bb2ce71adf5f3645437d2daad1854a25afcd5bf6e7bdc519de5c37f97ae, M = the submagma generated by {30, 84} (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 17:47:18 · history