Equation 677 Database

← all  ·  ← by size  ·  ← size 595

Magma 6cc8aef3a675…

magma 6cc8aef3a675
Size
595
Isomorphism class hash
6cc8aef3a67545f8d3a742ff9043d3849c1999d0318d83632e8089250c7f13c8
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 06:15:10
Display reorder
138,143,139,140,141,142,356,355,354,357,358,359,364,363,365,360,361,362,417,419,418,416,415,414,353,352,351,349,350,348,518,515,516,517,553,227,223,222,225,226,224,291,290,292,293,288,289,49,48,50,51,52,53,83,82,78,79,80,81,158,157,159,160,161,156,115,114,116,117,118,119,208,207,209,204,205,206,19,18,20,21,22,23,300,302,305,303,304,301,308,307,309,310,311,306,74,73,75,76,77,72,341,340,339,336,337,338,366,368,367,369,370,371,377,379,378,380,381,382,440,500,501,509,502,503,389,477,445,476,444,475,532,523,522,520,538,572,558,548,567,573,588,539,586,562,589,585,98,100,99,96,97,101,155,154,150,151,152,153,24,29,25,26,27,28,313,312,314,315,316,317,327,326,328,329,324,325,85,84,86,87,88,89,169,168,170,171,172,173,295,294,296,297,298,299,287,283,286,284,285,282,133,132,134,135,136,137,123,122,124,125,120,121,487,486,488,464,463,485,481,480,506,449,450,413,456,455,454,453,451,452,421,422,420,424,425,423,429,492,469,491,468,490,529,531,526,514,519,590,592,541,571,543,584,587,557,550,552,540,3,5,4,0,2,1,272,271,273,274,275,270,228,233,229,230,231,232,90,95,91,92,93,94,12,17,13,14,15,16,57,56,58,59,54,55,242,241,243,244,245,240,185,184,180,181,182,183,147,149,146,144,145,148,9,8,10,11,6,7,165,164,166,167,162,163,386,388,387,384,385,383,343,342,344,346,347,345,431,432,430,433,434,435,483,482,484,441,507,426,497,439,498,508,499,442,537,530,511,513,536,542,568,594,577,549,556,563,582,559,554,575,278,280,279,276,277,281,64,63,65,60,61,62,178,177,179,174,175,176,187,186,188,189,190,191,103,102,104,105,106,107,213,212,214,215,210,211,69,68,70,71,66,67,269,268,264,265,266,267,239,235,238,236,237,234,202,201,203,198,199,200,255,254,256,257,252,253,402,401,403,406,404,405,375,374,376,372,373,443,472,471,436,495,437,473,400,397,396,399,394,395,398,393,505,479,504,392,528,534,510,512,524,574,546,569,555,583,576,581,560,579,566,561,36,38,37,40,41,39,248,247,249,250,251,246,197,196,192,193,194,195,46,45,47,42,43,44,109,108,110,111,112,113,221,220,216,217,218,219,128,127,129,130,131,126,322,321,323,318,319,320,35,31,34,32,33,30,260,259,261,262,263,258,333,332,334,335,330,331,478,447,446,390,391,448,460,462,461,457,458,459,466,465,427,489,428,467,408,407,409,412,410,411,438,496,474,494,470,493,533,527,521,525,535,564,547,570,551,544,545,591,578,593,580,565 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#10d95f4d62da29d597cabb26c5d7a2889acb76e08f2897cdd164594c6bfbc5c4, M = the submagma generated by {36, 72} (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 06:15:11 · history