Equation 677 Database

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Magma 70c2a365ae8d…

magma 70c2a365ae8d
Size
381
Isomorphism class hash
70c2a365ae8d1f97e42eaa2cd4411759f609f6bbf26df3dcbd563fc5d0b5bdaf
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 23:27:05
Display reorder
380,70,69,71,66,67,68,324,325,326,327,328,329,11,12,7,8,9,10,59,54,55,56,57,58,48,49,50,51,52,53,275,280,285,291,296,270,64,65,60,61,62,63,261,266,240,245,251,256,215,221,226,231,236,210,201,206,180,185,191,196,150,176,156,161,166,171,344,334,361,339,370,357,346,375,345,365,145,144,146,147,142,143,311,306,307,308,309,310,136,137,138,139,140,141,126,127,128,129,130,131,125,120,121,122,123,124,278,283,288,293,299,274,1,149,133,134,135,132,264,269,244,248,253,258,218,224,229,234,239,214,204,209,183,189,194,199,154,179,158,163,169,174,352,333,363,336,373,359,354,378,353,368,3,2,4,5,6,0,301,300,302,303,304,305,107,102,103,104,105,106,116,117,118,119,114,115,110,111,112,113,108,109,276,281,286,290,295,271,99,100,101,96,97,98,260,265,241,246,250,255,216,220,225,230,235,211,200,205,181,186,190,195,151,175,155,160,165,170,332,351,360,350,372,356,330,377,338,367,24,23,19,20,21,22,317,312,313,314,315,316,41,36,37,38,39,40,25,148,29,26,27,28,44,45,46,47,42,43,279,284,289,294,298,273,33,34,35,30,31,32,263,268,243,249,254,259,219,223,228,233,238,213,203,208,184,188,193,198,153,178,159,164,168,173,337,343,364,331,374,358,341,379,342,369,17,16,18,13,14,15,321,322,323,318,319,320,89,84,85,86,87,88,75,76,77,72,73,74,92,93,94,95,90,91,277,282,287,292,297,272,81,82,83,78,79,80,262,267,242,247,252,257,217,222,227,232,237,212,202,207,182,187,192,197,152,177,157,162,167,172,348,349,362,347,371,355,340,376,335,366 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#51f9fa4941789fcec91b298b71630f6443ab313fec0bf96b206088496fe3251b, M = {75} 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 23:27:06 · history