Equation 677 Database

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Magma 04a2abd5b188…

magma 04a2abd5b188
Size
381
Isomorphism class hash
04a2abd5b188e7a2a1da671bf97919e2f55e276d3d6ec29ed80bce856d43e3d5
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 23:36:04
Display reorder
380,42,52,47,67,57,62,222,227,217,207,212,202,100,106,95,295,91,86,27,32,37,12,16,21,240,230,235,255,245,250,110,116,121,125,130,137,287,277,282,272,262,267,72,77,82,4,5,292,182,172,177,197,187,192,157,162,167,142,147,152,308,306,307,311,309,310,352,335,377,332,362,347,342,367,372,357,43,53,48,68,58,63,223,228,218,208,213,203,103,108,98,298,93,88,28,33,38,13,18,22,243,233,238,258,248,253,113,118,123,128,133,138,288,278,283,273,263,268,73,78,83,6,7,293,183,173,178,198,188,193,158,163,168,143,148,153,323,321,322,320,318,319,353,339,378,333,363,348,343,368,373,358,40,50,45,66,56,61,221,225,216,205,210,200,102,107,97,297,92,87,25,30,36,11,17,24,241,231,237,256,246,252,112,117,122,127,132,136,286,276,281,271,260,265,70,75,80,0,1,291,181,171,176,196,185,190,156,161,165,140,145,150,304,305,303,300,302,301,350,337,375,331,361,346,341,366,371,355,41,51,46,65,55,60,220,226,215,206,211,201,101,105,96,296,90,85,26,31,35,10,15,20,242,232,236,257,247,251,111,115,120,126,131,135,285,275,280,270,261,266,71,76,81,2,3,290,180,170,175,195,186,191,155,160,166,141,146,151,315,316,317,312,313,314,351,336,376,330,360,345,340,365,370,356,44,54,49,69,59,64,224,229,219,209,214,204,104,109,99,299,94,89,29,34,39,14,19,23,244,234,239,259,249,254,114,119,124,129,134,139,289,279,284,274,264,269,74,79,84,8,9,294,184,174,179,199,189,194,159,164,169,144,149,154,327,328,329,324,325,326,354,338,379,334,364,349,344,369,374,359 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#8e237b368ce49904371f47a0bbc192c3f49c4a8da81336b4c06fd9fdc3a5d75d, M = {73} 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 23:36:04 · history