Equation 677 Database

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Magma 21235102e604…

magma 21235102e604
Size
381
Isomorphism class hash
21235102e604d92cec41e80e0168437b593a3bcf0a34ca71382d6c587306c59c
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 23:21:53
Display reorder
380,162,152,142,17,7,2,172,182,192,252,232,242,112,122,127,132,87,97,77,318,320,321,323,282,262,272,202,212,222,46,65,26,31,55,36,60,291,157,147,22,12,167,187,237,247,107,82,102,319,277,257,197,207,70,51,137,287,177,227,117,92,322,267,217,41,295,332,376,352,342,337,364,347,356,373,367,161,151,141,15,6,0,170,180,190,250,230,240,110,121,126,131,85,95,76,303,305,301,302,281,261,271,201,211,221,45,66,25,30,56,35,61,290,156,146,20,11,166,185,235,245,106,80,100,304,276,255,195,206,71,50,135,285,175,226,115,90,300,266,216,40,296,331,379,350,340,335,362,345,355,372,369,163,153,143,18,8,3,173,183,193,253,233,243,113,123,128,133,88,98,78,306,308,309,311,283,263,273,203,213,223,48,68,28,33,58,38,63,293,158,148,23,13,168,188,238,248,108,83,103,307,278,258,198,208,73,53,138,288,178,228,118,93,310,268,218,43,298,330,375,351,341,336,361,346,358,371,366,164,154,144,19,9,4,174,184,194,254,234,244,114,124,129,134,89,99,79,327,325,326,329,284,264,274,204,214,224,49,69,29,34,59,39,64,294,159,149,24,14,169,189,239,249,109,84,104,328,279,259,199,209,74,54,139,289,179,229,119,94,324,269,219,44,299,334,378,354,344,339,363,349,359,370,365,160,150,140,16,5,1,171,181,191,251,231,241,111,120,125,130,86,96,75,312,314,315,317,280,260,270,200,210,220,47,67,27,32,57,37,62,292,155,145,21,10,165,186,236,246,105,81,101,313,275,256,196,205,72,52,136,286,176,225,116,91,316,265,215,42,297,333,377,353,343,338,360,348,357,374,368 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#4422b92082c5ba9f603861f57ee03bc11c9f901f0082cee83e1cd8bfe00bbd4d, M = {68} 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 23:21:54 · history