Equation 677 Database

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Magma b51d1ac2e8bc…

magma b51d1ac2e8bc
Size
381
Isomorphism class hash
b51d1ac2e8bc7ce6f654b2f527826634c2aeaf95b7ef91f8c46cca2d485e79b0
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 23:35:28
Display reorder
380,2,5,19,8,18,54,67,57,69,68,78,76,91,92,90,191,188,175,177,197,168,166,169,167,153,266,269,252,255,253,104,119,117,101,118,144,129,142,143,126,244,228,241,230,227,308,306,307,311,309,44,40,43,42,41,216,219,202,200,205,294,291,280,277,278,310,374,372,373,370,371,346,347,349,348,345,7,4,6,11,10,53,60,59,56,55,80,75,77,93,94,178,180,176,179,196,152,156,150,151,155,254,257,251,258,250,106,103,107,100,102,128,131,132,127,125,233,226,229,232,225,323,321,322,320,318,29,25,28,27,26,204,208,203,201,207,282,279,283,276,275,319,358,357,359,356,355,330,332,333,334,331,23,20,24,21,22,70,72,71,73,74,96,95,99,98,97,193,194,195,192,199,173,172,174,170,171,273,272,270,271,274,121,123,122,120,124,148,146,147,149,145,247,249,248,246,245,324,325,326,327,328,46,47,45,49,48,223,222,224,220,221,297,298,296,295,299,329,375,379,376,377,378,353,354,350,351,352,14,9,15,16,17,58,66,65,63,64,88,79,86,85,89,190,186,187,189,198,165,164,162,154,163,264,268,256,267,265,115,113,116,105,114,138,140,141,139,130,243,240,239,242,231,305,303,304,302,301,39,35,38,37,36,214,218,215,206,217,293,289,292,281,290,300,368,367,369,365,366,341,342,343,344,340,13,1,3,0,12,51,61,50,62,52,81,87,82,84,83,182,181,185,183,184,157,158,161,160,159,259,260,262,261,263,109,112,108,110,111,137,134,133,136,135,235,238,234,236,237,313,314,312,316,317,30,31,34,33,32,209,210,213,212,211,285,284,286,287,288,315,363,362,364,360,361,337,338,339,335,336 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 = {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 23:35:29 · history