Equation 677 Database

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Magma 4800cbb2f4e3…

magma 4800cbb2f4e3
Size
399
Isomorphism class hash
4800cbb2f4e3f3403a67c905e6904295e000a29635d4fd9850cea6b7a8f66738
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 16:48:21
Display reorder
47,48,49,50,51,52,53,45,46,40,41,42,43,44,36,37,38,39,381,54,109,78,112,55,111,114,79,56,113,80,116,57,115,72,118,58,117,73,120,59,119,74,122,60,121,75,125,61,123,76,108,62,124,77,110,94,87,63,99,96,88,64,101,98,89,65,103,100,81,66,105,102,82,67,107,104,83,68,91,69,106,84,93,90,85,70,95,92,86,71,97,392,386,385,391,221,158,297,333,222,159,334,298,223,160,299,335,224,161,300,336,216,153,301,337,217,154,302,338,218,155,303,339,219,156,304,340,220,157,305,341,151,290,230,326,152,291,231,327,144,292,232,328,145,293,233,329,146,294,225,330,147,295,226,331,227,148,296,332,149,288,228,324,150,289,229,325,384,390,389,383,306,175,141,237,307,176,238,142,308,177,143,239,309,178,135,240,310,179,136,241,311,171,137,242,312,172,138,234,313,173,139,235,314,174,140,236,168,134,315,246,169,126,316,247,170,127,317,248,162,128,318,249,163,129,319,250,164,130,320,251,321,165,131,243,166,132,322,244,167,133,323,245,387,398,397,388,206,272,349,342,198,273,344,351,199,274,353,346,200,275,355,348,201,276,357,350,202,277,359,352,203,278,343,354,204,270,345,356,205,271,347,358,281,367,215,360,282,369,207,362,283,371,208,364,284,373,209,366,285,375,210,368,286,376,211,370,212,287,361,372,279,363,213,374,280,365,214,377,393,395,396,394,19,191,11,252,20,192,253,12,21,193,13,254,22,194,14,255,23,195,15,256,24,196,16,257,25,197,17,258,26,189,9,259,18,190,10,260,184,4,28,261,185,5,29,262,186,6,30,263,187,7,31,264,188,8,32,265,180,1,33,266,34,181,0,267,182,2,35,268,183,3,27,269,380,382,379,378 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#4a5649c07d4ee0ffe5eba018e0359bb81d1d3dce2afe0de9cfd0cd05ba2d08a3, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 21.

last edited by qawbecrdtey at 2026-10-06 16:48:22 · history