Equation 677 Database

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Magma 4f5fad12b6c4…

magma 4f5fad12b6c4
Size
381
Isomorphism class hash
4f5fad12b6c49c63f7681f319bfe5b9697c37d35ae4f5ba186ab340008a328e7
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 23:28:30
Display reorder
380,72,82,77,90,85,221,311,309,310,308,306,307,100,105,96,225,116,111,9,232,8,292,11,10,236,240,245,250,255,260,275,266,270,295,280,285,145,136,141,134,121,127,171,175,166,155,160,151,201,206,196,185,190,180,26,30,20,211,41,36,60,65,56,216,50,45,341,360,371,331,367,336,346,350,375,357,73,83,78,92,87,222,324,325,326,327,328,329,102,107,97,227,117,112,13,233,12,293,14,15,238,243,248,253,258,263,278,268,273,298,283,288,148,138,143,132,123,128,173,178,168,158,163,153,203,208,198,188,193,183,27,33,23,212,42,35,63,68,58,217,51,47,342,363,373,333,368,337,347,352,377,358,74,84,79,93,88,223,322,323,321,319,320,318,103,108,98,228,118,113,17,234,16,294,18,19,239,244,249,254,259,264,279,269,274,299,284,289,149,139,144,133,124,129,174,179,169,159,164,154,204,209,199,189,194,184,28,34,24,213,43,38,64,69,59,218,52,48,343,364,374,334,369,338,348,353,378,359,70,81,76,91,86,220,317,315,316,314,312,313,101,106,95,226,115,110,2,230,3,291,1,0,235,241,247,251,257,261,276,265,271,296,281,286,146,135,140,130,120,125,170,176,165,156,161,150,200,205,195,186,191,181,25,31,21,210,40,37,61,66,55,215,54,46,340,361,370,330,366,335,345,351,379,355,71,80,75,94,89,224,305,303,304,302,301,300,104,109,99,229,119,114,5,231,4,290,6,7,237,242,246,252,256,262,277,267,272,297,282,287,147,137,142,131,122,126,172,177,167,157,162,152,202,207,197,187,192,182,29,32,22,214,44,39,62,67,57,219,53,49,344,362,372,332,365,339,349,354,376,356 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 = {76} 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 23:28:31 · history