Equation 677 Database

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Magma 52ed4f6b9ec8…

magma 52ed4f6b9ec8
Size
381
Isomorphism class hash
52ed4f6b9ec84b685b4f44da6aedb93db334968db641b93c30a70a934707d7e2
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 23:28:46
Display reorder
380,241,231,222,261,272,251,126,127,128,129,130,131,36,34,35,39,37,38,15,13,14,125,16,291,117,118,280,114,115,116,315,316,317,312,313,314,109,110,111,112,113,295,207,215,40,41,42,43,189,175,182,285,191,196,133,134,132,200,210,95,256,266,275,226,236,245,335,365,355,345,360,331,376,340,351,370,243,233,223,263,273,253,33,31,32,30,28,29,70,71,72,73,74,75,93,94,92,90,91,293,102,103,283,99,100,101,329,327,328,326,324,325,160,161,162,163,164,298,208,218,76,79,77,78,185,178,183,288,193,198,98,96,97,201,213,23,258,268,278,228,238,248,338,368,358,348,363,332,378,343,353,372,244,234,224,264,274,254,2,1,0,4,3,170,21,22,20,18,19,17,67,65,66,69,68,294,64,63,284,62,60,61,318,319,320,321,322,323,165,166,167,168,169,299,205,219,5,6,7,8,188,179,184,289,194,199,172,173,171,204,214,174,259,269,279,229,239,249,339,369,359,349,364,334,379,344,354,373,240,230,220,260,270,250,56,57,55,155,59,58,49,50,51,52,53,54,120,121,122,123,124,290,24,25,281,26,27,119,311,309,310,308,306,307,46,47,48,44,45,296,206,216,12,10,11,9,186,177,181,286,190,195,156,157,158,203,212,159,255,265,276,225,235,246,336,366,356,346,362,333,375,341,350,371,242,232,221,262,271,252,145,146,147,148,149,150,83,84,85,80,81,82,142,140,141,144,143,292,138,139,282,135,136,137,301,300,302,303,304,305,104,105,106,107,108,297,209,217,89,87,88,86,187,176,180,287,192,197,152,153,151,202,211,154,257,267,277,227,237,247,337,367,357,347,361,330,377,342,352,374 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 = {70} 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 23:28:47 · history