Equation 677 Database

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Magma a189f5ecdc3f…

magma a189f5ecdc3f
Size
381
Isomorphism class hash
a189f5ecdc3f76781062912d89fa8b4774c45a22e2dc7041b443b1f3ebf399c3
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 23:31:54
Display reorder
380,251,245,256,261,266,240,235,211,215,220,225,230,82,83,78,79,80,81,60,61,62,63,64,65,312,313,311,316,314,315,66,67,68,69,70,71,77,72,73,74,75,76,151,156,161,166,171,175,289,291,296,270,276,281,205,181,186,191,196,200,84,89,85,86,87,88,361,351,367,352,334,377,373,331,330,355,253,248,258,263,268,243,238,213,218,223,228,233,129,130,131,126,127,128,143,138,139,140,141,142,321,322,324,326,328,319,148,149,144,145,146,147,122,123,124,125,120,121,153,158,163,168,173,178,287,293,298,273,278,283,208,183,188,193,198,203,133,132,134,135,136,137,362,344,368,338,358,375,372,350,357,348,250,246,255,260,265,241,236,210,216,221,226,231,112,113,108,109,110,111,90,91,92,93,94,95,303,304,305,301,300,302,96,97,98,99,100,101,107,102,103,104,105,106,150,155,160,165,170,176,285,290,295,271,275,282,206,180,185,190,195,201,114,119,115,116,117,118,360,353,366,354,345,378,374,332,333,356,254,249,259,264,269,244,239,214,219,224,229,234,20,21,22,23,18,19,3,4,5,1,0,2,320,323,325,327,329,318,8,9,10,11,6,7,12,13,14,15,16,17,154,159,164,169,174,179,288,294,299,274,279,284,209,184,189,194,199,204,27,26,28,29,24,25,363,342,369,347,341,376,371,340,346,339,252,247,257,262,267,242,237,212,217,222,227,232,35,30,31,32,33,34,52,53,48,49,50,51,307,308,309,310,306,317,59,54,55,56,57,58,40,41,36,37,38,39,152,157,162,167,172,177,286,292,297,272,277,280,207,182,187,192,197,202,46,45,47,42,43,44,364,335,365,336,359,379,370,349,343,337 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 = {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 23:31:55 · history