Equation 677 Database

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Magma 95c1ab59f0d5…

magma 95c1ab59f0d5
Size
381
Isomorphism class hash
95c1ab59f0d5bfb09517e9a3902a8ba49f4fd9608aa0a34c62aa297082dd52b2
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 23:31:58
Display reorder
380,104,84,106,85,86,87,66,67,68,69,70,71,135,266,276,291,175,171,79,80,81,82,83,78,230,235,211,216,221,226,63,64,65,258,273,288,186,191,196,200,205,181,75,76,77,72,73,74,241,246,251,260,280,295,160,165,141,146,151,156,313,312,314,315,316,317,356,334,366,375,341,350,348,342,371,360,22,21,23,24,25,26,3,4,5,6,7,8,139,268,278,293,179,174,16,17,18,19,20,15,234,239,214,219,224,228,27,28,29,255,270,285,189,194,198,204,209,184,12,13,14,9,10,11,243,248,254,264,284,299,164,169,144,148,153,159,310,309,311,306,307,308,358,336,365,377,337,352,346,335,373,362,58,57,59,60,61,62,105,107,88,89,90,91,136,265,275,290,176,170,99,100,101,102,103,98,231,236,210,215,220,225,54,55,56,257,272,287,185,190,195,201,206,180,95,96,97,92,93,94,240,245,250,261,281,296,161,166,140,145,150,155,328,327,329,324,325,326,355,343,368,376,339,353,347,340,370,361,36,41,37,38,39,40,45,46,47,42,43,44,138,269,279,294,178,173,30,31,32,33,34,35,233,238,213,218,223,229,2,0,1,256,271,286,188,193,199,203,208,183,50,51,52,53,48,49,244,249,253,263,283,298,163,168,143,149,154,158,322,321,323,318,319,320,359,333,367,378,332,351,345,338,374,363,132,131,133,134,129,130,112,113,114,115,116,111,137,267,277,292,177,172,126,127,128,123,124,125,232,237,212,217,222,227,108,109,110,259,274,289,187,192,197,202,207,182,118,119,120,121,122,117,242,247,252,262,282,297,162,167,142,147,152,157,300,301,302,303,304,305,357,331,369,379,330,354,349,344,372,364 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#7eadf19d7b6e5946b2d6ebbbf061273ea953f89e2819b4463bfb57d0a1e47218, M = {67} 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 23:31:59 · history