Equation 677 Database

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Magma a5adeb6cd275…

magma a5adeb6cd275
Size
381
Isomorphism class hash
a5adeb6cd27518f398d6940909f7997b56c4a97e7aa6d5a6fe3575a1e3570629
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
no
Fiber matrix
symmetric: no · normal: no · rank: 331 (nullity 50) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:35:18
Display reorder
380,235,147,311,97,122,142,117,107,231,310,82,162,308,250,137,6,275,172,212,57,285,0,182,52,207,261,17,72,225,185,87,255,127,167,306,245,92,132,307,157,12,195,270,220,67,47,37,42,32,27,240,112,309,152,102,280,292,177,62,202,22,266,215,78,190,297,358,343,363,368,348,378,353,338,332,370,237,145,325,96,120,140,116,105,230,324,81,161,328,252,135,7,277,170,210,56,287,2,180,51,205,262,18,71,227,186,86,256,126,166,329,246,90,131,327,156,13,196,271,221,66,45,35,40,30,26,241,111,326,150,100,281,293,175,60,200,23,268,217,76,192,295,356,341,360,366,345,376,351,335,333,371,238,148,313,98,123,143,118,108,233,312,83,163,316,253,138,5,278,173,213,58,288,3,183,53,208,260,15,73,228,188,88,258,128,168,317,248,93,133,315,158,10,198,273,223,68,48,38,43,33,28,243,113,314,153,103,283,291,178,63,203,20,265,218,77,193,298,357,342,362,367,347,377,352,337,330,374,236,146,321,95,121,141,115,106,232,323,80,160,318,251,136,9,276,171,211,55,286,1,181,50,206,263,16,70,226,187,85,257,125,165,319,247,91,130,320,155,11,197,272,222,65,46,36,41,31,25,242,110,322,151,101,282,290,176,61,201,21,267,216,75,191,296,355,340,361,365,346,375,350,336,331,372,239,149,300,99,124,144,119,109,234,301,84,164,304,254,139,8,279,174,214,59,289,4,184,54,209,264,19,74,229,189,89,259,129,169,305,249,94,134,303,159,14,199,274,224,69,49,39,44,34,29,244,114,302,154,104,284,294,179,64,204,24,269,219,79,194,299,359,344,364,369,349,379,354,339,334,373 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#8d944e514216d4896f15b10e8d6cfc32a88a33c4742733ce5a4d2024a617afbd, 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 23:35:19 · history