Equation 677 Database

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Magma 267d62def983…

magma 267d62def983
Size
381
Isomorphism class hash
267d62def9839e2a1480269dcaaa24c71344a3eacf85124e534851619ff0c5ae
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 23:28:25
Display reorder
380,159,154,164,139,144,149,49,294,44,34,39,29,208,198,203,223,213,218,134,124,129,119,109,114,74,79,69,59,64,54,253,243,248,238,228,233,84,89,94,99,299,104,194,184,189,179,169,174,13,18,23,1,9,288,273,278,283,258,263,268,323,321,322,320,318,319,359,353,338,363,348,379,333,369,374,344,155,150,161,136,141,146,47,292,42,32,37,27,206,196,201,220,210,215,130,121,126,115,105,110,71,76,66,55,60,50,251,241,247,236,226,232,80,86,91,95,296,101,190,181,186,175,165,170,11,16,20,2,6,286,271,276,281,255,260,265,300,302,301,304,305,303,355,351,336,361,345,376,330,366,370,342,157,152,162,137,142,147,48,293,43,33,38,28,207,197,202,222,212,217,132,122,127,117,107,112,70,75,65,56,61,51,252,240,245,235,225,230,81,85,90,96,295,100,192,182,187,177,167,172,12,17,22,3,7,287,272,277,282,257,262,267,313,314,312,316,317,315,357,350,337,362,347,377,332,365,372,343,156,151,160,135,140,145,45,291,40,31,36,25,205,195,200,221,211,216,131,120,125,116,106,111,72,77,67,57,62,52,250,242,246,237,227,231,82,87,92,97,297,102,191,180,185,176,166,171,10,15,21,0,5,285,270,275,280,256,261,266,325,326,324,328,329,327,356,354,335,360,346,375,331,367,371,341,158,153,163,138,143,148,46,290,41,30,35,26,209,199,204,224,214,219,133,123,128,118,108,113,73,78,68,58,63,53,254,244,249,239,229,234,83,88,93,98,298,103,193,183,188,178,168,173,14,19,24,4,8,289,274,279,284,259,264,269,309,310,311,306,307,308,358,352,339,364,349,378,334,368,373,340 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 = {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 23:28:26 · history