Equation 677 Database

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Magma d9b5cf053b8f…

magma d9b5cf053b8f
Size
381
Isomorphism class hash
d9b5cf053b8fc67caa4bedb305d9694c3407d8adb8145fc3f93e901eefa0a30d
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 23:40:09
Display reorder
380,34,194,36,42,176,35,177,195,37,43,30,178,196,38,44,197,179,31,39,45,192,174,32,40,46,175,193,33,41,47,167,186,15,327,26,162,187,16,301,27,163,188,17,300,28,164,189,12,321,29,165,190,13,322,24,166,191,14,310,25,184,180,181,182,183,185,376,350,348,375,378,377,351,352,349,379,114,240,58,90,168,115,169,241,59,91,116,170,242,54,92,243,171,117,55,93,244,172,118,56,94,173,245,119,57,95,222,208,72,324,22,223,209,73,325,23,224,204,74,320,18,225,205,75,319,19,226,206,76,326,20,227,207,77,309,21,266,268,269,264,265,267,369,353,354,356,357,368,331,330,342,355,5,216,109,70,198,1,199,217,110,71,0,200,218,111,66,219,201,2,112,67,220,202,3,113,68,203,221,4,108,69,236,261,86,328,52,237,262,87,302,53,238,263,88,306,48,239,258,89,303,49,234,259,84,307,50,235,260,85,304,51,150,153,154,155,151,152,370,344,347,374,372,371,345,346,343,373,140,285,9,135,273,141,274,286,10,136,142,275,287,11,137,282,270,143,6,132,283,271,138,7,133,272,284,139,8,134,247,161,97,318,121,248,156,98,308,122,249,157,99,305,123,250,158,100,317,124,251,159,101,323,125,246,160,96,311,120,290,292,293,288,289,291,363,338,341,367,365,364,339,340,337,366,130,228,61,82,253,131,254,229,62,83,126,255,230,63,78,231,256,127,64,79,232,257,128,65,80,252,233,129,60,81,294,211,144,312,107,295,212,145,313,102,296,213,146,314,103,297,214,147,315,104,298,215,148,316,105,299,210,149,329,106,276,278,279,280,281,277,362,332,335,361,359,358,333,334,336,360 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#ae56d720edba524495de2abbf45bb01a29474b7517905dc2fe3202c6dddb6f97, 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 23:40:10 · history