Equation 677 Database

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Magma 684422e900fd…

magma 684422e900fd
Size
381
Isomorphism class hash
684422e900fdb5a1406197124c44621f5a06bb0309dff56770e93167b6c67057
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 23:45:46
Display reorder
380,96,102,290,116,106,112,136,141,145,120,125,130,295,21,26,41,32,37,280,70,75,80,86,92,8,271,9,6,210,7,61,240,66,47,52,55,302,301,300,305,303,304,191,181,186,205,195,200,175,165,170,161,151,156,251,257,246,267,277,262,216,225,221,286,231,236,330,355,335,351,346,360,367,340,376,374,95,101,291,117,107,111,137,142,147,122,127,132,296,20,25,40,30,35,281,71,76,81,87,91,13,270,12,11,211,10,62,242,67,46,50,57,307,308,306,310,311,309,192,182,187,207,197,202,177,167,172,162,152,157,250,255,245,266,276,261,215,226,220,285,230,235,332,356,336,350,345,362,365,341,375,370,97,100,292,115,105,110,135,140,146,121,126,131,297,22,27,42,33,38,282,72,77,84,88,93,15,272,14,0,212,1,60,241,65,45,51,56,322,323,321,319,320,318,190,180,185,206,196,201,176,166,171,160,150,155,252,256,247,265,275,260,217,227,222,287,232,237,331,357,337,352,347,361,366,342,378,371,99,104,294,119,109,114,139,144,149,124,129,134,299,24,29,44,34,39,284,74,79,83,89,94,19,274,18,4,214,5,64,244,69,49,54,59,326,324,325,329,327,328,194,184,189,209,199,204,179,169,174,164,154,159,254,259,249,269,279,264,219,229,224,289,234,239,334,359,339,354,349,364,369,344,379,373,98,103,293,118,108,113,138,143,148,123,128,133,298,23,28,43,31,36,283,73,78,82,85,90,17,273,16,2,213,3,63,243,68,48,53,58,315,316,317,312,313,314,193,183,188,208,198,203,178,168,173,163,153,158,253,258,248,268,278,263,218,228,223,288,233,238,333,358,338,353,348,363,368,343,377,372 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#dba6afe67f86b36e533f777300b41b8ae8b2a840d4529c92a6cd7ab996e48d4f, M = {74} 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 23:45:47 · history