Equation 677 Database

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Magma 944d4fd45a1a…

magma 944d4fd45a1a
Size
381
Isomorphism class hash
944d4fd45a1aa832c985c5f6aa8445283956bdd7334b5139fe595e432eee47ad
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 23:17:41
Display reorder
380,26,25,24,23,291,22,195,200,205,211,216,221,235,226,231,250,240,245,105,96,100,120,111,116,15,16,17,18,19,186,29,30,28,62,27,257,191,8,9,285,20,21,161,166,156,175,180,170,270,261,265,295,276,280,140,145,151,126,131,136,312,313,314,315,316,317,336,361,365,341,379,355,346,330,351,371,49,48,47,51,290,50,197,202,207,212,217,222,237,227,232,251,241,248,109,97,102,122,112,117,40,41,42,43,44,187,31,32,33,34,63,256,192,7,6,287,45,46,162,167,157,177,182,172,272,262,267,297,277,282,142,147,152,127,132,137,311,309,310,308,306,307,337,362,367,342,376,356,345,332,352,372,74,77,73,76,293,75,198,203,208,213,218,223,238,228,233,253,243,247,107,98,103,123,113,118,64,65,66,67,68,188,78,79,80,81,82,258,193,69,70,288,71,72,163,168,158,178,183,173,273,263,268,298,278,283,143,148,153,128,133,138,304,305,303,300,302,301,338,363,368,343,377,358,348,333,353,373,53,56,52,55,292,54,196,201,206,210,215,220,236,225,230,252,242,246,106,95,101,121,110,115,10,11,12,13,14,185,57,58,59,60,61,255,190,1,0,286,2,3,160,165,155,176,181,171,271,260,266,296,275,281,141,146,150,125,130,135,322,323,321,319,320,318,335,360,366,340,375,357,347,331,350,370,85,84,83,87,294,86,199,204,209,214,219,224,239,229,234,254,244,249,108,99,104,124,114,119,88,89,90,91,92,189,35,36,37,38,39,259,194,5,4,289,93,94,164,169,159,179,184,174,274,264,269,299,279,284,144,149,154,129,134,139,327,328,329,324,325,326,339,364,369,344,378,359,349,334,354,374 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#0c1c8b18119133fb8debdb5d149d6db1ac93e4c65e1bffaee2a0311d537b261b, 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 23:17:42 · history