Equation 677 Database

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Magma 9d1c49de2ef9…

magma 9d1c49de2ef9
Size
381
Isomorphism class hash
9d1c49de2ef9925749bdf1c72b711e19a83343b283270d75a18a5fc0dc4b2773
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 23:46:49
Display reorder
380,246,255,251,275,261,210,27,30,28,29,43,44,241,46,47,266,271,45,25,295,24,22,23,21,215,221,226,230,236,285,306,307,308,309,310,311,192,182,187,207,197,202,103,108,98,293,118,113,148,138,143,133,123,128,85,91,81,76,280,71,173,168,178,153,158,163,362,365,355,335,353,373,340,345,332,376,247,257,252,277,262,213,65,63,64,62,15,14,242,18,16,267,273,17,12,299,13,9,10,11,218,223,228,233,238,288,316,317,315,313,314,312,193,183,188,208,198,203,100,106,95,290,116,111,145,135,140,131,121,126,87,92,84,77,282,72,170,165,175,151,156,161,360,367,359,338,350,370,342,348,333,377,248,258,253,278,263,212,50,49,48,51,58,57,243,61,59,268,272,60,55,298,56,52,53,54,217,222,227,232,237,287,304,305,303,300,302,301,191,181,186,206,195,201,101,105,96,291,115,110,146,136,141,130,120,125,88,93,80,78,283,73,171,166,176,150,155,160,361,368,358,337,351,371,343,347,331,378,245,256,250,276,260,211,31,32,19,20,41,42,240,38,39,265,270,40,37,297,36,34,35,33,216,220,225,231,235,286,325,326,324,328,329,327,190,180,185,205,196,200,102,107,97,292,117,112,147,137,142,132,122,127,86,90,83,75,281,70,172,167,177,152,157,162,363,366,357,336,352,372,341,346,330,375,249,259,254,279,264,214,69,68,66,67,7,8,244,4,5,269,274,6,3,296,2,0,26,1,219,224,229,234,239,289,319,320,318,322,323,321,194,184,189,209,199,204,104,109,99,294,119,114,149,139,144,134,124,129,89,94,82,79,284,74,174,169,179,154,159,164,364,369,356,339,354,374,344,349,334,379 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#e1df87152eb4e0a2aee101822e1e35ad774d7a93b5a84f6ade065ecc70777444, M = {66} 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 23:46:50 · history