Equation 677 Database

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Magma 7a8b3aa6fe02…

magma 7a8b3aa6fe02
Size
381
Isomorphism class hash
7a8b3aa6fe02aef99a38958c7d0835b4607eda81138dd81788ea02c9ee0853e0
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 23:33:20
Display reorder
380,206,158,256,6,56,106,28,78,128,183,228,278,238,288,38,88,138,193,103,155,203,253,3,53,243,298,48,98,148,198,328,323,324,325,326,327,33,83,133,188,233,283,254,4,54,104,156,204,42,92,142,164,247,292,105,157,205,255,5,55,52,2,252,102,154,202,331,378,349,367,374,363,350,339,340,332,219,172,269,19,69,119,29,79,129,184,229,279,239,289,39,89,139,194,117,170,217,267,17,67,244,299,49,99,149,199,305,301,300,302,303,304,34,84,134,189,234,284,266,16,66,116,169,216,44,94,144,179,249,294,118,171,218,268,18,68,70,20,270,120,173,220,342,375,345,369,373,341,337,357,359,358,201,151,251,1,51,101,27,77,127,182,227,277,237,287,37,87,137,192,112,165,212,262,12,62,242,297,47,97,147,197,311,306,307,308,309,310,32,82,132,187,232,282,263,13,63,113,166,213,40,90,141,153,246,291,114,167,214,264,14,64,65,15,265,115,168,215,335,377,356,366,372,362,330,364,354,355,211,163,261,11,61,111,26,76,126,181,225,275,236,286,36,86,136,190,107,159,207,257,7,57,240,295,45,95,146,196,318,329,322,319,320,321,31,81,130,185,231,281,259,9,59,109,161,209,43,93,143,178,248,293,110,162,210,260,10,60,58,8,258,108,160,208,346,379,338,368,370,334,352,343,351,353,221,174,271,21,71,121,25,75,125,180,226,276,235,285,35,85,135,191,100,152,200,250,0,50,241,296,46,96,145,195,312,313,314,315,316,317,30,80,131,186,230,280,273,23,73,123,176,223,41,91,140,150,245,290,124,177,224,274,24,74,72,22,272,122,175,222,336,376,360,365,371,348,347,333,344,361 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#81fb02f374018e52eb43ccfa7482c1ceb3842f71095f08d9a76873470f8f397e, M = {74} 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 23:33:21 · history