Equation 677 Database

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Magma 2a0c2863eccd…

magma 2a0c2863eccd
Size
381
Isomorphism class hash
2a0c2863eccdf9ec93b8256d192b4c09ab3c1427c276eda3db178dfea9a924f3
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 23:29:06
Display reorder
380,160,171,167,185,177,181,217,207,211,201,191,197,156,145,150,141,130,135,311,309,310,308,306,307,48,53,58,63,288,68,1,296,3,91,95,86,283,28,23,38,43,32,227,232,222,241,245,236,105,110,101,120,125,115,251,256,262,266,271,275,15,293,14,78,83,73,348,356,338,372,354,331,360,377,342,366,161,170,165,188,175,183,215,205,210,200,193,195,157,147,152,142,132,137,323,321,322,320,318,319,46,51,57,61,285,66,5,297,4,92,96,87,282,27,22,37,40,31,226,231,221,243,248,238,107,111,100,121,127,117,250,255,260,267,272,277,9,291,8,75,80,70,346,358,337,370,350,333,363,376,343,368,162,172,166,186,176,180,216,206,212,202,190,196,155,146,151,140,131,136,304,305,303,300,302,301,47,50,56,60,286,65,2,295,0,90,97,85,281,25,20,36,42,34,225,230,220,240,246,235,106,112,102,122,126,116,252,257,261,265,270,276,11,290,10,76,81,71,345,355,336,371,351,330,361,375,341,365,164,174,169,189,179,184,219,209,214,204,194,199,159,149,154,144,134,139,317,315,316,314,312,313,49,54,59,64,289,69,19,299,18,93,99,88,284,29,24,39,44,33,229,234,224,244,249,239,109,114,104,124,129,119,254,259,264,269,274,279,17,294,16,79,84,74,349,359,339,374,353,334,364,379,344,369,163,173,168,187,178,182,218,208,213,203,192,198,158,148,153,143,133,138,324,325,326,327,328,329,45,52,55,62,287,67,7,298,6,94,98,89,280,26,21,35,41,30,228,233,223,242,247,237,108,113,103,123,128,118,253,258,263,268,273,278,13,292,12,77,82,72,347,357,335,373,352,332,362,378,340,367 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#5a9d04a9c7b116e670149859ec35e9ea984c3e29c9284ef9fa55ee11860b9239, M = {75} 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 23:29:07 · history