Equation 677 Database

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Magma 1d39735e2bce…

magma 1d39735e2bce
Size
595
Isomorphism class hash
1d39735e2bce73ed995d129a0cd7ee05ec0ddcef2f3d4f8c00310cf407d2e653
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 04:52:33
Display reorder
16,13,17,12,15,14,124,123,119,120,121,122,11,10,6,7,8,9,301,313,302,305,303,304,403,383,384,380,381,382,511,517,565,581,554,243,242,174,244,245,241,159,75,71,72,73,74,61,60,56,57,58,59,126,125,127,217,218,164,206,205,204,160,94,95,109,108,110,111,112,211,170,234,232,233,226,171,215,214,216,163,212,213,505,504,506,508,509,507,287,289,288,286,284,285,426,425,427,429,430,428,329,331,330,334,332,333,340,339,338,337,335,336,280,279,278,281,282,283,449,316,315,416,417,418,498,500,499,502,503,501,550,549,519,510,523,520,521,522,563,582,593,574,575,564,578,573,21,20,22,23,18,19,99,98,100,101,96,97,93,92,88,89,90,91,76,81,77,78,79,80,29,28,24,25,26,27,51,50,52,53,54,193,208,162,209,210,207,161,182,181,152,183,184,180,431,433,432,445,443,444,399,398,397,401,402,400,409,408,407,405,406,404,494,493,492,496,497,495,379,378,377,376,374,375,258,259,260,263,261,262,487,488,486,489,490,491,457,458,456,460,461,459,535,526,514,551,548,524,516,515,568,566,579,555,557,571,570,572,44,43,45,40,41,42,139,138,140,135,136,137,102,107,103,104,105,106,85,84,86,87,82,83,1,0,2,3,4,5,146,145,147,148,149,257,255,246,256,249,248,175,254,253,247,250,251,252,434,436,435,448,446,447,442,441,440,438,439,437,277,276,275,360,352,353,356,355,354,358,361,357,266,265,264,268,267,312,350,359,351,348,349,347,341,343,342,344,345,346,371,373,372,369,370,368,540,541,534,533,530,532,531,513,577,567,583,552,594,589,584,576,33,32,34,35,30,31,39,188,189,190,154,187,177,151,176,150,178,179,186,185,153,37,38,36,143,142,144,141,240,235,172,239,236,237,173,238,166,221,222,219,220,165,230,229,231,169,227,228,474,479,480,475,481,482,271,270,269,273,274,272,414,413,415,410,411,412,394,396,395,393,391,392,450,452,451,453,454,455,300,299,298,295,296,297,423,422,424,420,421,419,469,468,484,483,485,470,545,547,536,528,518,525,529,527,553,588,559,591,592,558,590,585,113,118,114,115,116,117,55,196,197,155,194,195,198,157,199,200,156,201,203,202,158,63,64,62,47,46,48,49,192,191,223,225,167,224,168,134,129,128,130,131,132,133,69,68,70,65,66,67,322,321,320,319,317,318,310,309,314,306,307,308,328,327,326,324,325,323,477,473,478,472,471,476,385,387,386,388,389,390,366,365,367,364,362,363,462,464,463,465,466,467,291,290,292,311,293,294,542,543,512,544,546,537,538,539,561,569,580,556,587,560,562,586 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#92768bb2ce71adf5f3645437d2daad1854a25afcd5bf6e7bdc519de5c37f97ae, 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 04:52:34 · history