Equation 677 Database

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Magma e3b750ce716f…

magma e3b750ce716f
Size
381
Isomorphism class hash
e3b750ce716f014bb6e3944e6ec45780dc28bad50b2bfefd40e0b42d99b0d1b1
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 23:26:36
Display reorder
380,275,205,285,295,195,200,151,156,161,135,141,146,270,280,290,42,43,44,28,29,24,25,26,27,37,38,39,40,41,36,236,210,215,220,226,231,175,180,185,190,166,170,240,246,251,256,261,266,31,32,33,34,35,30,99,100,103,105,107,98,322,329,323,324,325,326,343,331,369,334,357,337,373,363,376,351,279,209,289,299,199,204,154,159,164,139,144,149,273,283,293,94,95,96,77,78,79,80,81,76,93,88,89,90,91,92,239,214,219,224,229,234,179,184,189,194,169,174,244,249,254,259,264,269,87,82,83,84,85,86,101,102,104,106,97,75,311,310,306,307,308,309,348,335,368,347,358,338,371,360,379,354,277,207,287,297,198,202,152,158,163,138,142,147,272,282,292,72,73,74,57,58,59,54,55,56,69,70,71,66,67,68,237,212,218,223,227,232,177,182,188,193,168,172,243,247,252,257,262,267,63,64,65,60,61,62,53,48,49,50,51,52,315,314,328,312,327,313,339,333,367,345,355,344,370,361,378,353,278,208,288,298,197,203,153,157,162,137,143,148,274,284,294,122,120,121,133,134,129,130,131,132,118,119,114,115,116,117,238,213,217,222,228,233,178,183,187,192,167,173,242,248,253,258,263,268,112,113,108,109,110,111,126,127,128,123,124,125,319,318,320,321,316,317,349,332,366,336,359,346,374,364,377,352,276,206,286,296,196,201,150,155,160,136,140,145,271,281,291,45,46,47,20,21,22,23,18,19,5,1,0,2,3,4,235,211,216,221,225,230,176,181,186,191,165,171,241,245,250,255,260,265,6,8,9,10,11,7,12,13,14,15,16,17,305,304,301,300,302,303,341,330,365,342,356,340,372,362,375,350 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#51f9fa4941789fcec91b298b71630f6443ab313fec0bf96b206088496fe3251b, M = {68} 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 23:26:37 · history