Equation 677 Database

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Magma be3889a307a9…

magma be3889a307a9
Size
381
Isomorphism class hash
be3889a307a9882815da5a81b68e1a8ece20ff9a49d6d822c94794854b5c2241
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 23:37:58
Display reorder
380,301,302,300,305,303,304,143,133,138,158,148,153,51,56,60,65,291,70,235,227,232,251,241,246,40,286,45,26,31,39,220,8,9,7,5,6,121,126,115,106,111,101,80,85,75,296,95,90,195,200,190,211,216,206,176,181,186,160,165,170,271,281,276,265,256,261,355,361,341,335,346,351,365,370,331,375,307,306,308,309,310,311,141,130,135,156,145,150,50,55,61,66,290,71,236,225,230,250,240,245,41,285,46,25,30,36,221,1,0,4,2,3,120,125,116,105,110,100,81,86,76,295,96,91,196,201,191,210,215,205,175,180,185,161,166,171,270,280,275,266,257,262,356,360,340,336,345,350,366,371,330,376,326,325,324,328,329,327,144,134,139,159,149,154,52,57,62,67,292,72,238,226,231,253,243,248,42,287,47,28,33,35,223,18,19,17,15,16,122,127,117,107,112,102,82,87,77,297,97,92,197,202,192,212,217,207,177,182,187,162,167,172,273,283,278,268,258,263,358,362,342,338,347,352,368,372,332,377,314,313,312,316,317,315,142,132,137,157,147,152,53,58,63,68,293,73,237,228,233,252,242,247,43,288,48,27,32,37,222,13,14,12,10,11,123,128,118,108,113,103,83,88,78,298,98,93,198,203,193,213,218,208,178,183,188,163,168,173,272,282,277,267,259,264,357,363,343,337,348,353,367,374,333,378,323,322,321,319,320,318,140,131,136,155,146,151,54,59,64,69,294,74,239,229,234,254,244,249,44,289,49,29,34,38,224,23,24,22,20,21,124,129,119,109,114,104,84,89,79,299,99,94,199,204,194,214,219,209,179,184,189,164,169,174,274,284,279,269,255,260,359,364,344,339,349,354,369,373,334,379 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#9f798321a12a7c259b4293859981bcb696138223932c95126c1c0ef29c354b2f, 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 23:37:59 · history