Equation 677 Database

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Magma bef5613d16ec…

magma bef5613d16ec
Size
381
Isomorphism class hash
bef5613d16ec2b8ea70d59eebc6c72f563e1abe0bbd6b3b5141ee26ccd7b367c
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: yes · rank: 301 (nullity 80) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:42:02
Display reorder
380,15,17,16,14,12,13,160,159,158,162,163,164,165,166,167,153,154,155,156,157,140,141,142,143,144,145,146,147,148,149,150,151,152,138,139,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,161,374,359,356,375,357,358,372,354,355,373,0,1,2,3,4,5,105,104,103,107,93,94,95,96,97,98,99,100,101,102,85,86,87,88,89,90,91,92,78,79,80,81,82,83,84,120,121,122,108,109,110,111,112,113,114,115,116,117,118,119,135,136,137,123,124,125,126,127,128,129,130,131,132,133,134,106,379,371,378,366,367,368,369,376,370,377,228,230,229,233,231,232,63,77,76,65,66,67,68,69,70,71,72,73,74,75,58,59,60,61,62,48,49,50,51,52,53,54,55,56,57,286,287,288,289,290,291,292,293,279,280,281,282,283,284,285,268,269,270,271,272,273,274,275,276,277,278,264,265,266,267,64,347,346,348,349,350,351,352,353,344,345,10,9,11,6,7,8,205,204,203,207,208,209,210,211,212,198,199,200,201,202,218,219,220,221,222,223,224,225,226,227,213,214,215,216,217,240,241,242,243,244,245,246,247,248,234,235,236,237,238,239,255,256,257,258,259,260,261,262,263,249,250,251,252,253,254,206,360,340,363,364,341,342,343,361,362,365,329,328,327,325,326,324,18,32,31,20,21,22,23,24,25,26,27,28,29,30,46,47,33,34,35,36,37,38,39,40,41,42,43,44,45,193,194,195,196,197,183,184,185,186,187,188,189,190,191,192,175,176,177,178,179,180,181,182,168,169,170,171,172,173,174,19,333,332,334,335,336,337,338,339,331,330 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#ba2659e3d875edec9a58973d1e5a59a409e503dd8379d7758e48aa8aa91fe243, M = {76} 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 23:42:03 · history