Equation 677 Database

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Magma f491a4aee1b6…

magma f491a4aee1b6
Size
381
Isomorphism class hash
f491a4aee1b6dedc79847c04610fc2922382dcbe81a338f3ad0bb5b4fbbef064
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:29:10
Display reorder
380,303,193,180,189,197,184,206,188,202,198,304,194,181,190,195,185,204,186,203,199,200,192,305,182,191,196,183,205,187,201,223,301,210,219,227,214,236,218,232,228,300,224,211,220,225,215,234,216,233,229,230,222,302,212,221,226,213,235,217,231,239,237,208,209,207,238,343,344,359,369,370,357,345,356,378,358,321,40,58,36,44,31,53,35,49,45,322,41,59,37,42,32,51,33,50,46,47,39,329,57,38,43,30,52,34,48,10,318,28,6,14,0,23,5,19,15,319,11,29,7,12,2,21,3,20,16,17,9,320,27,8,13,1,22,4,18,26,24,55,56,54,25,341,352,377,367,353,342,340,368,354,355,316,62,80,89,63,81,72,85,71,67,317,60,78,87,64,82,73,86,69,68,66,61,315,79,88,65,83,74,84,70,92,313,110,119,93,111,102,115,101,97,314,90,108,117,94,112,103,116,99,98,96,91,312,109,118,95,113,104,114,100,105,106,77,75,76,107,330,339,373,379,338,351,337,346,371,366,327,266,241,258,271,245,289,253,284,276,328,264,242,259,272,243,290,257,282,277,278,265,326,240,260,270,244,288,252,283,267,324,246,263,274,250,292,256,285,281,325,268,247,261,275,251,293,254,286,279,280,269,323,248,262,273,249,291,255,287,298,299,295,296,294,297,364,335,349,363,376,334,336,350,375,365,307,152,170,179,153,171,162,175,161,157,308,150,168,177,154,172,163,176,159,158,156,151,306,169,178,155,173,164,174,160,122,310,140,149,123,141,132,145,131,127,311,120,138,147,124,142,133,146,129,128,126,121,309,139,148,125,143,134,144,130,135,136,167,165,166,137,372,374,361,362,333,332,360,348,331,347 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#5da407abe4e69ea2e8e77e634a9a34d8ab5d7df6477bcbd8c80289a0abfd3c16, M = {66} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:29:11 · history